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FINITENESS OF CANONICAL QUOTIENTS OF DEHN QUANDLES OF SURFACES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-03-11 NEERAJ K. DHANWANI, MAHENDER SINGH
The Dehn quandle of a closed orientable surface is the set of isotopy classes of nonseparating simple closed curves with a natural quandle structure arising from Dehn twists. In this paper, we consider the finiteness of some canonical quotients of these quandles. For a surface of positive genus, we give a precise description of the 2-quandle of its Dehn quandle. Further, with some exceptions for genus
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RADU GROUPS ACTING ON TREES ARE CCR J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-03-06 LANCELOT SEMAL
We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting $2$ -transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for $(d_0,d_1)$ -semi-regular trees such that $d_0,d_1\in \Theta $ , where $\Theta $ is an asymptotically dense set
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THE -GENERATION OF THE FINITE SIMPLE ODD-DIMENSIONAL ORTHOGONAL GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-02-28 MARCO ANTONIO PELLEGRINI, MARIA CHIARA TAMBURINI BELLANI
The complete classification of the finite simple groups that are $(2,3)$ -generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$ -generators for the finite odd-dimensional orthogonal groups $\Omega _{2k+1}(q)$ , $k\geq 4$ . As a byproduct, we also obtain $(2,3)$ -generators for $\Omega _{4k}^+(q)$ with $k\geq 3$ and q odd, and for $\Omega _{4k+2}^\pm (q)$
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ON THE ITERATIONS AND THE ARGUMENT DISTRIBUTION OF MEROMORPHIC FUNCTIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-02-15 JIE DING, JIANHUA ZHENG
This paper consists of two parts. The first is to study the existence of a point a at the intersection of the Julia set and the escaping set such that a goes to infinity under iterates along Julia directions or Borel directions. Additionally, we find such points that approximate all Borel directions to escape if the meromorphic functions have positive lower order. We confirm the existence of such slowly
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THE RIEFFEL CORRESPONDENCE FOR EQUIVALENT FELL BUNDLES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-01-17 S. KALISZEWSKI, JOHN QUIGG, DANA P. WILLIAMS
We establish a generalized Rieffel correspondence for ideals in equivalent Fell bundles.
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A WEIGHTED ESTIMATE OF COMMUTATORS OF BOCHNER–RIESZ OPERATORS FOR HERMITE OPERATOR J. Aust. Math. Soc. (IF 0.7) Pub Date : 2024-01-15 PENG CHEN, XIXI LIN
Let H be the Hermite operator $-\Delta +|x|^2$ on $\mathbb {R}^n$ . We prove a weighted $L^2$ estimate of the maximal commutator operator $\sup _{R>0}|[b, S_R^\lambda (H)](f)|$ , where $ [b, S_R^\lambda (H)](f) = bS_R^\lambda (H) f - S_R^\lambda (H)(bf) $ is the commutator of a BMO function b and the Bochner–Riesz means $S_R^\lambda (H)$ for the Hermite operator H. As an application, we obtain the
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THE PRO--SOLVABLE TOPOLOGY ON A FREE GROUP J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-22 CLAUDE MARION, PEDRO V. SILVA, GARETH TRACEY
We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable
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NORMAL SUBMONOIDS AND CONGRUENCES ON A MONOID J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-18 JOSEP ELGUETA
A notion of normal submonoid of a monoid M is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set $\mathsf {NorSub}(M)$ of normal submonoids of M is a complete lattice. Joins are explicitly described and the lattice is computed for the finite full transformation monoids $T_n$ , $n\geq ~1$ . It is also shown that $\mathsf {NorSub}(M)$ is modular for a specific
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QUALITATIVE UNCERTAINTY PRINCIPLE ON CERTAIN LIE GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-18 ARUP CHATTOPADHYAY, DEBKUMAR GIRI, R. K. SRIVASTAVA
In this article, we study the recent development of the qualitative uncertainty principle on certain Lie groups. In particular, we consider that if the Weyl transform on certain step-two nilpotent Lie groups is of finite rank, then the function has to be zero almost everywhere as long as the nonvanishing set for the function has finite measure. Further, we consider that if the Weyl transform of each
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BRATTELI–VERSHIKISABILITY OF POLYGONAL BILLIARDS ON THE HYPERBOLIC PLANE J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-15 ANIMA NAGAR, PRADEEP SINGH
Bratteli–Vershik models of compact, invertible zero-dimensional systems have been well studied. We take up such a study for polygonal billiards on the hyperbolic plane, thus considering these models beyond zero-dimensions. We describe the associated Bratteli models and show that these billiard dynamics can be described by Vershik maps.
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FINITELY PRESENTED INVERSE SEMIGROUPS WITH FINITELY MANY IDEMPOTENTS IN EACH -CLASS AND NON-HAUSDORFF UNIVERSAL GROUPOIDS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-13 PEDRO V. SILVA, BENJAMIN STEINBERG
The complex algebra of an inverse semigroup with finitely many idempotents in each $\mathcal D$ -class is stably finite by a result of Munn. This can be proved fairly easily using $C^{*}$ -algebras for inverse semigroups satisfying this condition that have a Hausdorff universal groupoid, or more generally for direct limits of inverse semigroups satisfying this condition and having Hausdorff universal
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COMMON ZEROS OF IRREDUCIBLE CHARACTERS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-11 NGUYEN N. HUNG, ALEXANDER MORETÓ, LUCIA MOROTTI
We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups $\mathsf {S}_n$ , it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this phenomenon, we introduce the common-zero graph of a finite group G, with nonlinear irreducible characters of G as vertices, and edges connecting characters
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RODRIGUES FORMULA AND LINEAR INDEPENDENCE FOR VALUES OF HYPERGEOMETRIC FUNCTIONS WITH VARYING PARAMETERS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-12-05 MAKOTO KAWASHIMA
In this article, we prove a generalized Rodrigues formula for a wide class of holonomic Laurent series, which yields a new linear independence criterion concerning their values at algebraic points. This generalization yields a new construction of Padé approximations including those for Gauss hypergeometric functions. In particular, we obtain a linear independence criterion over a number field concerning
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SOME GLOBAL EXISTENCE RESULTS ON LOCALLY FINITE GRAPHS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-11-06 SHOUDONG MAN, GUOQING ZHANG
Let $G=(V, E)$ be a locally finite graph with the vertex set V and the edge set E, where both V and E are infinite sets. By dividing the graph G into a sequence of finite subgraphs, the existence of a sequence of local solutions to several equations involving the p-Laplacian and the poly-Laplacian systems is confirmed on each subgraph, and the global existence for each equation on graph G is derived
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FAITHFULNESS OF THE 2-BRAID GROUP VIA ZIGZAG ALGEBRA IN TYPE B J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-10-27 EDMUND HENG, KIE SENG NGE
We show that a certain category of bimodules over a finite-dimensional quiver algebra known as a type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier’s conjecture on the faithfulness of the 2-braid groups for type B.
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MULTIPLIERS ON COMMUTATIVE HYPERGROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-10-18 VISHVESH KUMAR, MICHAEL RUZHANSKY
The main purpose of this paper is to prove Hörmander’s $L^p$–$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff–Young–Paley inequality for commutative hypergroups. We show the $L^p$–$L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chébli–Trimèche
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TORIC REFLECTION GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-10-18 THOMAS GOBET
Several finite complex reflection groups have a braid group that is isomorphic to a torus knot group. The reflection group is obtained from the torus knot group by declaring meridians to have order k for some $k\geq 2$, and meridians are mapped to reflections. We study all possible quotients of torus knot groups obtained by requiring meridians to have finite order. Using the theory of J-groups of Achar
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AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-09-19 MICHAELA CULLY-HUGILL, ADRIAN W. DUDEK
This paper gives an explicit version of Selberg’s mean-value estimate for the prime number theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to short-interval results for primes and for Goldbach numbers. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32\,277\log ^2 y]$ for at least half the $y\in [x,2x]$ for all $x\geq 2$ , and at least one
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ON THE GEOMETRY OF SPACELIKE MEAN CURVATURE FLOW SOLITONS IMMERSED IN A GRW SPACETIME J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-09-15 HENRIQUE F. DE LIMA, WALLACE F. GOMES, MÁRCIO S. SANTOS, MARCO ANTONIO L. VELÁSQUEZ
We investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-I\times _{f}M^n$, with base $I\subset \mathbb R$, Riemannian fiber $M^n$ and warping function $f\in C^\infty (I)$. For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space
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GHOSTS AND CONGRUENCES FOR -APPROXIMATIONS OF HYPERGEOMETRIC PERIODS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-08-02 ALEXANDER VARCHENKO, WADIM ZUDILIN
We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers
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HALL CLASSES OF GROUPS WITH A LOCALLY FINITE OBSTRUCTION J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-07-24 F. DE GIOVANNI, M. TROMBETTI, B. A. F. WEHRFRITZ
A well-known theorem of Philip Hall states that if a group G has a nilpotent normal subgroup N such that $G/N'$ is nilpotent, then G itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group G admitting a nilpotent normal subgroup N such that $G/N'$ belongs to 𝔛. Hall classes have been considered by several authors, such as Plotkin [‘Some properties of automorphisms
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WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-07-18 TAPENDU RANA
We prove Wiener Tauberian theorem type results for various spaces of radial functions, which are Banach algebras on a real-rank-one semisimple Lie group G. These are natural generalizations of the Wiener Tauberian theorem for the commutative Banach algebra of the integrable radial functions on G.
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ON POSSIBLE VALUES OF THE INTERIOR ANGLE BETWEEN INTERMEDIATE SUBALGEBRAS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-07-17 VED PRAKASH GUPTA, DEEPIKA SHARMA
We show that all values in the interval $[0,{\pi }/{2}]$ can be attained as interior angles between intermediate subalgebras (as introduced by Bakshi and the first named author [‘Lattice of intermediate subalgebras’, J. Lond. Math. Soc. (2)104(2) (2021), 2082–2127]) of a certain inclusion of simple unital $C^*$ -algebras. We also calculate the interior angles between intermediate crossed product subalgebras
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CONDITIONAL FLATNESS, FIBERWISE LOCALIZATIONS, AND ADMISSIBLE REFLECTIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-06-23 MARINO GRAN, JÉRÔME SCHERER
We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localization, analogous results to those obtained in the category of groups hold, and we provide existence theorems for certain localization functors in specific
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RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-05-29 LEA BENEISH, DEBANJANA KUNDU, ANWESH RAY
Let p be a prime. In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of degree p. We also study growth of the p-primary Selmer group and the Shafarevich–Tate group in cyclic degree-p extensions and improve upon previously known results in this direction.
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NONREALIZABILITY OF CERTAIN REPRESENTATIONS IN FUSION SYSTEMS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-04-11 BOB OLIVER
For a finite abelian p-group A and a subgroup $\Gamma \le \operatorname {\mathrm {Aut}}(A)$, we say that the pair $(\Gamma ,A)$ is fusion realizable if there is a saturated fusion system ${\mathcal {F}}$ over a finite p-group $S\ge A$ such that $C_S(A)=A$, $\operatorname {\mathrm {Aut}}_{{\mathcal {F}}}(A)=\Gamma $ as subgroups of $\operatorname {\mathrm {Aut}}(A)$, and . In this paper, we develop
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MULTIPLICATION TABLES AND WORD-HYPERBOLICITY IN FREE PRODUCTS OF SEMIGROUPS, MONOIDS AND GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-03-17 CARL-FREDRIK NYBERG-BRODDA
This article studies the properties of word-hyperbolic semigroups and monoids, that is, those having context-free multiplication tables with respect to a regular combing, as defined by Duncan and Gilman [‘Word hyperbolic semigroups’, Math. Proc. Cambridge Philos. Soc. 136(3) (2004), 513–524]. In particular, the preservation of word-hyperbolicity under taking free products is considered. Under mild
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AN INCIDENCE RESULT FOR WELL-SPACED ATOMS IN ALL DIMENSIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-02-20 PETER J. BRADSHAW
We prove an incidence result counting the k-rich $\delta $-tubes induced by a well-spaced set of $\delta $-atoms. Our result coincides with the bound that would be heuristically predicted by the Szemerédi–Trotter theorem and holds in all dimensions $d \geq 2$. We also prove an analogue of Beck’s theorem for $\delta $-atoms and $\delta $-tubes as an application of our result.
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ON THE NUMBER OF QUADRATIC ORTHOMORPHISMS THAT PRODUCE MAXIMALLY NONASSOCIATIVE QUASIGROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-02-20 ALEŠ DRÁPAL, IAN M. WANLESS
Let q be an odd prime power and suppose that $a,b\in \mathbb {F}_q$ are such that $ab$ and $(1{-}a)(1{-}b)$ are nonzero squares. Let $Q_{a,b} = (\mathbb {F}_q,*)$ be the quasigroup in which the operation is defined by $u*v=u+a(v{-}u)$ if $v-u$ is a square, and $u*v=u+b(v{-}u)$ if $v-u$ is a nonsquare. This quasigroup is called maximally nonassociative if it satisfies $x*(y*z) = (x*y)*z \Leftrightarrow
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SEMIRING AND INVOLUTION IDENTITIES OF POWER GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2023-01-17 SERGEY V. GUSEV, MIKHAIL V. VOLKOV
For every group G, the set $\mathcal {P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup $ and element-wise multiplication $\cdot $, and forms an involution semigroup under $\cdot $ and element-wise inversion ${}^{-1}$. We show that if the group G is finite, non-Dedekind, and solvable, neither the semiring $(\mathcal {P}(G),\cup ,\cdot )$ nor the involution semigroup $(\mathcal
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COSUPPORT FOR COMPACTLY GENERATED TRIANGULATED CATEGORIES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-12-13 XIAOYAN YANG
The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations of cosupport, and get some results that, in special cases, recover and generalize the known results about the usual cosupport. Additionally, we include some computations
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ON THE ALGEBRAS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-12-12 REZA ESMAILVANDI, MEHDI NEMATI, NAGESWARAN SHRAVAN KUMAR
Let H be an ultraspherical hypergroup and let $A(H)$ be the Fourier algebra associated with $H.$ In this paper, we study the dual and the double dual of $A(H).$ We prove among other things that the subspace of all uniformly continuous functionals on $A(H)$ forms a $C^*$-algebra. We also prove that the double dual $A(H)^{\ast \ast }$ is neither commutative nor semisimple with respect to the Arens product
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ELLIPTIC COHOMOLOGY IS UNIQUE UP TO HOMOTOPY J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-11-15 J. M. DAVIES
Homotopy theory folklore tells us that the sheaf defining the cohomology theory $\operatorname {\mathrm {Tmf}}$ of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of $\operatorname {\mathrm {Tmf}}$.
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PERMUTATION-BASED PRESENTATIONS FOR BRIN’S HIGHER-DIMENSIONAL THOMPSON GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-11-15 MARTYN QUICK
The higher-dimensional Thompson groups $nV$, for $n \geqslant 2$, were introduced by Brin [‘Presentations of higher dimensional Thompson groups’, J. Algebra 284 (2005), 520–558]. We provide new presentations for each of these infinite simple groups. The first is an infinite presentation, analogous to the Coxeter presentation for the finite symmetric group, with generating set equal to the set of transpositions
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AUTOMORPHISMS AND SYMPLECTIC LEAVES OF CALOGERO–MOSER SPACES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-10-17 CÉDRIC BONNAFÉ
We study the symplectic leaves of the subvariety of fixed points of an automorphism of a Calogero–Moser space induced by an element of finite order of the normalizer of the associated complex reflection group. We give a parametrization à la Harish-Chandra of its symplectic leaves (generalizing earlier works of Bellamy and Losev). This result is inspired by the mysterious relations between the geometry
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SIMPLY CONNECTED MANIFOLDS WITH LARGE HOMOTOPY STABLE CLASSES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-09-26 ANTHONY CONWAY, DIARMUID CROWLEY, MARK POWELL, JOERG SIXT
For every $k \geq 2$ and $n \geq 2$, we construct n pairwise homotopically inequivalent simply connected, closed $4k$-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In dimension four, we exhibit an analogous phenomenon for spin$^{c}$ structures on $S^2 \times S^2$. For $m\geq 1$, we
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CHARACTER STACKS ARE PORC COUNT J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-09-23 NICK BRIDGER, MASOUD KAMGARPOUR
We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a polynomial on residue classes (PORC). The key ingredients in the proof are Lusztig’s Jordan decomposition of complex characters of finite reductive groups and Deriziotis’s results on their genus numbers. As a consequence
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GROUPS ACTING ON TREES WITH PRESCRIBED LOCAL ACTION J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-09-12 STEPHAN TORNIER
We extend the Burger–Mozes theory of closed, nondiscrete, locally quasiprimitive automorphism groups of locally finite, connected graphs to the semiprimitive case, and develop a generalization of Burger–Mozes universal groups acting on the regular tree $T_{d}$ of degree $d\in \mathbb {N}_{\ge 3}$. Three applications are given. First, we characterize the automorphism types that the quasicentre of a
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LEAVITT PATH ALGEBRAS OF WEIGHTED AND SEPARATED GRAPHS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-09-12 PERE ARA
In this paper, we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related. We prove that any Leavitt path algebra $L(E,\omega )$ of a row-finite vertex weighted graph $(E,\omega )$ is $*$-isomorphic to the lower Leavitt path algebra of a certain bipartite separated graph $(E(\omega ),C(\omega ))$. For a general locally finite weighted
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BOUNDARY BLOW-UP SOLUTIONS TO EQUATIONS INVOLVING THE INFINITY LAPLACIAN J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-08-23 CUICUI LI, FANG LIU, PEIBIAO ZHAO
In this paper, we study the boundary blow-up problem related to the infinity Laplacian $$ \begin{align*}\begin{cases} \Delta_{\infty}^h u=u^q &\mathrm{in}\; \Omega, \\ u=\infty &\mathrm{on} \;\partial\Omega, \end{cases} \end{align*} $$ where $\Delta _{\infty }^h u=|Du|^{h-3} \langle D^2uDu,Du \rangle $ is the highly degenerate and h-homogeneous operator associated with the infinity Laplacian arising
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DESCRIPTION OF GROWTH AND OSCILLATION OF SOLUTIONS OF COMPLEX LDE’S J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-06-16 IGOR CHYZHYKOV, JANNE GRÖHN, JANNE HEITTOKANGAS, JOUNI RÄTTYÄ
It is known that, in the unit disc as well as in the whole complex plane, the growth of the analytic coefficients $A_0,\dotsc ,A_{k-2}$ of $$ \begin{align*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0, \quad k\geqslant 2, \end{align*} $$determines, under certain growth restrictions, not only the growth but also the oscillation of the equation’s nontrivial solutions, and vice versa. A uniform
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REGULARITY OF AML FUNCTIONS IN TWO-DIMENSIONAL NORMED SPACES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-05-20 SEBASTIÁN TAPIA-GARCÍA
Savin [‘ $\mathcal {C}^{1}$ regularity for infinity harmonic functions in two dimensions’, Arch. Ration. Mech. Anal. 3(176) (2005), 351–361] proved that every planar absolutely minimizing Lipschitz (AML) function is continuously differentiable whenever the ambient space is Euclidean. More recently, Peng et al. [‘Regularity of absolute minimizers for continuous convex Hamiltonians’, J. Differential
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BOUNDED COHOMOLOGY AND BINATE GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-05-10 FRANCESCO FOURNIER-FACIO, CLARA LÖH, MARCO MORASCHINI
A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes in all positive degrees. Amenable groups are boundedly acyclic, while the first nonamenable examples are the group of compactly supported homeomorphisms of $ {\mathbb {R}}^{n}$ (Matsumoto–Morita) and mitotic groups (Löh). We prove that binate (alias pseudo-mitotic) groups are boundedly acyclic, which provides
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RATIONAL -ALGEBRAS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-05-10 APURVA SETH, PRAHLAD VAIDYANATHAN
We show that the properties of being rationally K-stable passes from the fibres of a continuous $C(X)$-algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action
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CAYLEY–ABELS GRAPHS AND INVARIANTS OF TOTALLY DISCONNECTED, LOCALLY COMPACT GROUPS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-04-13 ARNBJÖRG SOFFÍA ÁRNADÓTTIR, WALTRAUD LEDERLE, RÖGNVALDUR G. MÖLLER
A connected, locally finite graph $\Gamma $ is a Cayley–Abels graph for a totally disconnected, locally compact group G if G acts vertex-transitively on $\Gamma $ with compact, open vertex stabilizers. Define the minimal degree of G as the minimal degree of a Cayley–Abels graph of G. We relate the minimal degree in various ways to the modular function, the scale function and the structure of compact
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REPRESENTING STRUCTURED SEMIGROUPS ON ÉTALE GROUPOID BUNDLES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-04-13 TRISTAN BICE
We examine a semigroup analogue of the Kumjian–Renault representation of C*-algebras with Cartan subalgebras on twisted groupoids. Specifically, we represent semigroups with distinguished normal subsemigroups as ‘slice-sections’ of groupoid bundles.
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SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-04-06 ROSTISLAV GRIGORCHUK, DMYTRO SAVCHUK
The ring $\mathbb Z_{d}$ of d-adic integers has a natural interpretation as the boundary of a rooted d-ary tree $T_{d}$ . Endomorphisms of this tree (that is, solenoidal maps) are in one-to-one correspondence with 1-Lipschitz mappings from $\mathbb Z_{d}$ to itself. In the case when $d=p$ is prime, Anashin [‘Automata finiteness criterion in terms of van der Put series of automata functions’,p-Adic
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COMPACT AND HILBERT–SCHMIDT WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-22 CHING-ON LO, ANTHONY WAI-KEUNG LOH
Let u and $\varphi $ be two analytic functions on the unit disk D such that $\varphi (D) \subset D$ . A weighted composition operator $uC_{\varphi }$ induced by u and $\varphi $ is defined on $A^2_{\alpha }$ , the weighted Bergman space of D, by $uC_{\varphi }f := u \cdot f \circ \varphi $ for every $f \in A^2_{\alpha }$ . We obtain sufficient conditions for the compactness of $uC_{\varphi }$ in terms
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HIGHER-DIMENSIONAL SHRINKING TARGET PROBLEM FOR BETA DYNAMICAL SYSTEMS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-22 MUMTAZ HUSSAIN, WEILIANG WANG
We consider the two-dimensional shrinking target problem in beta dynamical systems (for general $\beta>1$ ) with general errors of approximation. Let $f, g$ be two positive continuous functions. For any $x_0,y_0\in [0,1]$ , define the shrinking target set $$ \begin{align*}E(T_\beta, f,g):=\left\{(x,y)\in [0,1]^2: \begin{array}{@{}ll@{}} \lvert T_{\beta}^{n}x-x_{0}\rvert
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SUBSHIFTS OF FINITE TYPE WITH A HOLE J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-22 HARITHA CHERIYATH, NIKITA AGARWAL
We consider a subshift of finite type on q symbols with a union of t cylinders based at words of identical length p as the hole. We explore the relationship between the escape rate into the hole and a rational function, $r(z)$, of correlations between forbidden words in the subshift with the hole. In particular, we prove that there exists a constant $D(t,p)$ such that if $q>D(t,p)$, then the escape
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RETRACTED - THE KRONECKER–WEYL EQUIDISTRIBUTION THEOREM AND GEODESICS IN 3-MANIFOLDS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-21 J. BECK, W. W. L. CHEN
Given any rectangular polyhedron $3$ -manifold $\mathcal {P}$ tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in $\mathcal {P}$ .
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-ALGEBRAS FROM GROUP REPRESENTATIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-08 VALENTIN DEACONU
We introduce certain $C^*$ -algebras and k-graphs associated to k finite-dimensional unitary representations $\rho _1,\ldots ,\rho _k$ of a compact group G. We define a higher rank Doplicher-Roberts algebra $\mathcal {O}_{\rho _1,\ldots ,\rho _k}$ , constructed from intertwiners of tensor powers of these representations. Under certain conditions, we show that this $C^*$ -algebra is isomorphic to a
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BOUNDEDNESS AND COMPACTNESS OF CAUCHY-TYPE INTEGRAL COMMUTATOR ON WEIGHTED MORREY SPACES J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-03-08 RUMING GONG, MANASA N. VEMPATI, QINGYAN WU, PEIZHU XIE
In this paper we study boundedness and compactness characterizations of the commutators of Cauchy type integrals on bounded strongly pseudoconvex domains D in $\mathbb C^{n}$ with boundaries $bD$ satisfying the minimum regularity condition $C^{2}$ , based on the recent results of Lanzani–Stein and Duong et al. We point out that in this setting the Cauchy type integral is the sum of the essential part
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LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE -FUNCTIONS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-02-22 PENG GAO, LIANGYI ZHAO
In this paper, we study lower-order terms of the one-level density of low-lying zeros of quadratic Hecke L-functions in the Gaussian field. Assuming the generalized Riemann hypothesis, our result is valid for even test functions whose Fourier transforms are supported in $(-2, 2)$ . Moreover, we apply the ratios conjecture of L-functions to derive these lower-order terms as well. Up to the first lower-order
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FINITE TWO-DISTANCE-TRANSITIVE DIHEDRANTS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-01-26 WEI JIN, LI TAN
A noncomplete graph is $2$ -distance-transitive if, for $i \in \{1,2\}$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance i in the graph, there exists an element of the graph automorphism group that maps $(u_1,v_1)$ to $(u_2,v_2)$ . This paper determines the family of $2$ -distance-transitive Cayley graphs over dihedral groups, and it is shown that if the girth of such
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GAPS IN THE THUE–MORSE WORD J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-01-25 LUKAS SPIEGELHOFER
The Thue–Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors w within this sequence, or more precisely, the sequence of gaps between consecutive occurrences. This gap sequence is morphic; we prove that it is not automatic as soon as the length of w is at least $2$ , thereby answering a question by J. Shallit
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SOME HOMOLOGICAL PROPERTIES OF CATEGORY FOR LIE SUPERALGEBRAS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2022-01-21 CHIH-WHI CHEN, VOLODYMYR MAZORCHUK
For classical Lie superalgebras of type I, we provide necessary and sufficient conditions for a Verma supermodule $\Delta (\lambda )$ to be such that every nonzero homomorphism from another Verma supermodule to $\Delta (\lambda )$ is injective. This is applied to describe the socle of the cokernel of an inclusion of Verma supermodules over the periplectic Lie superalgebras $\mathfrak {pe} (n)$ and
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AN EFFECTIVE ANALYTIC FORMULA FOR THE NUMBER OF DISTINCT IRREDUCIBLE FACTORS OF A POLYNOMIAL J. Aust. Math. Soc. (IF 0.7) Pub Date : 2021-12-09 STEPHAN RAMON GARCIA, ETHAN SIMPSON LEE, JOSH SUH, JIAHUI YU
We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial $f \in \mathbb {Z}[x]$ . We use an explicit version of Mertens’ theorem for number fields to estimate a related sum over rational primes. For a given $f \in \mathbb {Z}[x]$ , our result yields a finite list of primes that certifies the number of distinct irreducible factors
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ON HIGHER DIMENSIONAL ARITHMETIC PROGRESSIONS IN MEYER SETS J. Aust. Math. Soc. (IF 0.7) Pub Date : 2021-12-06 ANNA KLICK, NICOLAE STRUNGARU
In this paper we study the existence of higher dimensional arithmetic progressions in Meyer sets. We show that the case when the ratios are linearly dependent over ${\mathbb Z}$ is trivial and focus on arithmetic progressions for which the ratios are linearly independent. Given a Meyer set $\Lambda $ and a fully Euclidean model set with the property that finitely many translates of cover $\Lambda $
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SMALL-SCALE EQUIDISTRIBUTION OF RANDOM WAVES GENERATED BY AN UNFAIR COIN FLIP J. Aust. Math. Soc. (IF 0.7) Pub Date : 2021-11-29 MIRIAM J. LEONHARDT, MELISSA TACY
In this paper we study the small-scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is, the coefficients take value $+1$ with probability p and $-1$ with probability $1-p$ . Random waves whose coefficients are associated with a fair coin are known to equidistribute down to the wavelength scale. We obtain explicit requirements on the deviation from