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  • Irreducible Decomposition of powers of edge ideals
    J. Algebra (IF 0.666) Pub Date : 2020-04-06
    Marcel Morales; Nguyen Thi Dung

    In this paper by using some tools from graph theory, mainly the theorem on ear decomposition of factor-critical graphs given by L. Lovász and the canonical decomposition of a graph given by Edmonds and Gallai, we can describe each irreducible component of powers of edge ideals of a graph. As an application we use our results to persistence of irreducible components, to bound dstab and to count the

    更新日期:2020-04-06
  • Automorphisms of descending mod-p central series
    J. Algebra (IF 0.666) Pub Date : 2020-04-03
    Ricard Riba

    In this paper we study the automorphism group of the quotient Nk• of a free group Γ of finite rank n by the (k+1)-term Γk+1• of the Zassenhaus (•=Z) and the Stallings (•=S) mod-p central series, with p a prime number. Just like in the already known case for the usual terms of the lower central series, these automorphism groups fit naturally into a short exact sequence containing the automorphism groups

    更新日期:2020-04-03
  • Algebraic entropy for amenable semigroup actions
    J. Algebra (IF 0.666) Pub Date : 2020-04-02
    Dikran Dikranjan; Antongiulio Fornasiero; Anna Giordano Bruno

    We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups S on discrete abelian groups A by endomorphisms; these extend the classical algebraic entropy for endomorphisms of abelian groups, corresponding to the case S=N. We investigate the fundamental properties of the algebraic entropy and compute it in several examples, paying special attention to the case

    更新日期:2020-04-03
  • On the classification of higher Auslander algebras for Nakayama algebras
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Dag Oskar Madsen; René Marczinzik; Gjergji Zaimi

    We give new improved bounds for the dominant dimension of Nakayama algebras and use those bounds to give a classification of Nakayama algebras with n simple modules that are higher Auslander algebras with global dimension at least n. The classification is then used to extend the results on the inequality for the global dimension of Nakayama algebras obtained in [18].

    更新日期:2020-04-03
  • On heights of characters of finite groups
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Zhicheng Feng; Yanjun Liu; Jiping Zhang

    In this paper we first state a conjecture on the lower bound of the maximal height of characters in a p-block of a finite group. Then we show that our conjecture holds for all blocks of covering groups of a sporadic simple group, for all blocks of a quasi-simple group G with G/Z(G) isomorphic to A6,A7 or a simple group of Lie type with an exceptional covering group, for all blocks of a symmetric group

    更新日期:2020-04-03
  • Actions of quantum linear spaces on quantum algebras
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Zachary Cline; Jason Gaddis

    We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra.

    更新日期:2020-04-03
  • Noncommutative Poisson bialgebras
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Jiefeng Liu; Chengming Bai; Yunhe Sheng

    In this paper, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebras. Using quasi-representations and the corresponding cohomology theory of noncommutative Poisson algebras, we study coboundary noncommutative Poisson bialgebras which leads to the introduction of the Poisson Yang-Baxter

    更新日期:2020-04-03
  • Lefschetz Properties and Hyperplane Arrangements
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Elisa Palezzato; Michele Torielli

    In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in the Artinian case hold also in this more general setting. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements.

    更新日期:2020-04-01
  • Representation ring of Levi subgroups versus cohomology ring of flag varieties II
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Shrawan Kumar; Sean Rogers

    For any reductive group G and a parabolic subgroup P with its Levi subgroup L, the first author in [5] introduced a ring homomorphism ξλP:Repλ−polyC(L)→H⁎(G/P,C), where Repλ−polyC(L) is a certain subring of the complexified representation ring of L (depending upon the choice of an irreducible representation V(λ) of G with highest weight λ). In this paper we study this homomorphism for G=Sp(2n) and

    更新日期:2020-04-01
  • Cohomology groups of Fermat curves via ray class fields of cyclotomic fields
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Rachel Davis; Rachel Pries

    The absolute Galois group of the cyclotomic field K=Q(ζp) acts on the étale homology of the Fermat curve X of exponent p. We study a Galois cohomology group which is valuable for measuring an obstruction for K-rational points on X. We analyze a 2-nilpotent extension of K which contains the information needed for measuring this obstruction. We determine a large subquotient of this Galois cohomology

    更新日期:2020-04-01
  • Algebraic differential formulas for the shuffle, stuffle and duality relations of iterated integrals
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Minoru Hirose; Nobuo Sato

    In this paper, we prove certain algebraic identities, which correspond to differentiation of the shuffle relation, the stuffle relation, and the relations which arise from Möbius transformations of iterated integrals. These formulas provide fundamental and useful tools in the study of iterated integrals on a punctured projective line.

    更新日期:2020-04-01
  • Hilbert's fourteenth problem and field modifications
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Shigeru Kuroda

    Let k(x)=k(x1,…,xn) be the rational function field, and k⊂L⊂k(x) an intermediate field. Hilbert's fourteenth problem asks whether the k-algebra L∩k[x1,…,xn] is finitely generated. Various counterexamples to this problem were already given, but there are still many open cases. In this paper, we study the problem in terms of the field-theoretic properties of L. Our result implies that, for any S⊂k[x1

    更新日期:2020-04-01
  • Indecomposable Jordan types of Loewy length 2
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Daniel Bissinger

    Let k be an algebraically closed field, char(k)=p≥2 and Er be a elementary abelian p-group of rank r≥2. Let (c,d)∈N2. We show that there exists an indecomposable module of constant Jordan type [1]c[2]d and Loewy length 2 if and only if qΓr(d,d+c)≤1 and c≥r−1, where qΓr(x,y):=x2+y2−rxy denotes the Tits form of the generalized Kronecker quiver Γr. Since p>2 and constant Jordan type [1]c[2]d imply Loewy

    更新日期:2020-04-01
  • A cohomological treatise of HKG-covers with applications to the Nottingham group
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Aristides Kontogeorgis; Ioannis Tsouknidas

    We characterize Harbater-Katz-Gabber curves in terms of a family of cohomology classes satisfying a compatibility condition. Our construction is applied to the description of finite subgroups of the Nottingham Group.

    更新日期:2020-04-01
  • Some Orbits of Free Words that are Determined by Measures on Finite Groups
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Liam Hanany; Chen Meiri; Doron Puder

    Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of AutF. A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [PP15]. Here we extend

    更新日期:2020-04-01
  • Fully inert subgroups of torsion-complete p-groups
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Brendan Goldsmith; Luigi Salce

    The main result of this paper states that fully inert subgroups of torsion-complete abelian p-groups are commensurable with fully invariant subgroups, which have a satisfactory characterization by a classical result by Kaplansky. As the proof of this fact relies on the analogous result for direct sums of cyclic p-groups, we provide revisited and simplified proofs of the fact that fully inert subgroups

    更新日期:2020-04-01
  • On the number of irreducible real-valued characters of a finite group
    J. Algebra (IF 0.666) Pub Date : 2020-04-01
    Nguyen Ngoc Hung; A.A. Schaeffer Fry; Hung P. Tong-Viet; C. Ryan Vinroot

    We prove that there exists an integer-valued function f on positive integers such that if a finite group G has at most k real-valued irreducible characters, then |G/Sol(G)|≤f(k), where Sol(G) denotes the largest solvable normal subgroup of G. In the case k=5, we further classify G/Sol(G). This partly answers a question of Iwasaki [15] on the relationship between the structure of a finite group and

    更新日期:2020-04-01
  • Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Vyacheslav Futorny; Dimitar Grantcharov; Luis Enrique Ramirez; Pablo Zadunaisky

    We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module

    更新日期:2020-04-01
  • Full rank presentations and nilpotent groups: structure, Diophantine problem, and genericity
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Albert Garreta; Alexei Miasnikov; Denis Ovchinnikov

    We study finitely generated nilpotent groups G given by full rank finite presentations 〈A|R〉Nc in the variety Nc of nilpotent groups of class at most c, where c≥2. We prove that if the deficiency |A|−|R| is at least 2 then the group G is virtually free nilpotent, it is quasi finitely axiomatizable (in particular, first-order rigid), and it is almost (up to finite factors) directly indecomposable. One

    更新日期:2020-04-01
  • Hypersurfaces with defect
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Niels Lindner

    A projective hypersurface X⊆Pn has defect if hi(X)≠hi(Pn) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P4 is not Q-factorial. We show that hypersurfaces with defect tend to be very singular: In characteristic 0, we present a lower bound on the Tjurina number, where X is allowed to have arbitrary isolated singularities. For X with mild singularities, we prove

    更新日期:2020-03-31
  • Decomposition algebras and axial algebras
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Tom De Medts; Simon F. Peacock; Sergey Shpectorov; Michiel Van Couwenberghe

    We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field, thereby allowing repetition of eigenvalues; (2) They allow for decompositions that do not arise from multiplication by idempotents; (3) They admit a natural notion

    更新日期:2020-03-31
  • Algebras defined by equations
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Peter M. Higgins; Marcel Jackson

    We show that an elementary class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular semigroups this allows an interpretation of a universal algebraic nature that is formulated entirely in terms of the associative binary operation of the semigroup

    更新日期:2020-03-31
  • Castelnuovo-Mumford regularity of representations of certain product categories
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Wee Liang Gan; Liping Li

    We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if they are presented in finite degrees, and hence the category consisting of them is abelian. These results apply to examples such as the categories FIm and FIGm.

    更新日期:2020-03-31
  • Ulrich ideals and 2-AGL rings
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Shiro Goto; Ryotaro Isobe; Naoki Taniguchi

    The notion of 2-almost Gorenstein local ring (2-AGL ring for short) is a generalization of the notion of almost Gorenstein local ring from the point of view of Sally modules of canonical ideals. In this paper, for further developments of the theory, we discuss three different topics on 2-AGL rings. The first one is to clarify the structure of minimal presentations of canonical ideals, and the second

    更新日期:2020-03-31
  • On the Cantor–Bendixson rank of the Grigorchuk group and the Gupta–Sidki 3 group
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Rachel Skipper; Phillip Wesolek

    We study the Cantor–Bendixson rank of the space of subgroups for members of a general class of finitely generated self-replicating branch groups. In particular, we show for G either the Grigorchuk group or the Gupta–Sidki 3 group, the Cantor–Bendixson rank of Sub(G) is ω. For each natural number n, we additionally characterize the subgroups of rank n and give a description of subgroups in the perfect

    更新日期:2020-03-31
  • The loop-stable homotopy category of algebras
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Emanuel Rodríguez Cirone

    Let ℓ be a commutative ring with unit. Garkusha constructed a functor from the category of ℓ-algebras into a triangulated category D, that is a universal excisive and homotopy invariant homology theory. Later on, he provided different descriptions of D, as an application of his motivic homotopy theory of algebras. Using these, it can be shown that D is triangulated equivalent to a category, denote

    更新日期:2020-03-31
  • Kac-Moody Groups and Completions
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Inna Capdeboscq; Dmitriy Rumynin

    In this paper we construct a new “pro-p-complete” topological Kac-Moody group and compare it to various known topological Kac-Moody groups. We come across this group by investigating the process of completion of groups with BN-pairs. We would like to know whether the completion of such a group admits a BN-pair. We give explicit criteria for this to happen.

    更新日期:2020-03-31
  • The weak Lefschetz property of equigenerated monomial ideals
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Nasrin Altafi; Mats Boij

    We determine a sharp lower bound for the Hilbert function in degree d of a monomial algebra failing the weak Lefschetz property over a polynomial ring with n variables and generated in degree d, for any d≥2 and n≥3. We consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group Z/dZ, for any n≥3 and

    更新日期:2020-03-31
  • On 3-dimensional complex Hom-Lie algebras
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    R. García-Delgado; G. Salgado; O.A. Sánchez-Valenzuela

    We study and classify the 3-dimensional Hom-Lie algebras over C. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space g. The well known Lie brackets for the 3-dimensional Lie algebras are included into appropriate isomorphism classes of such products representatives. For each product representative

    更新日期:2020-03-31
  • 1-Auslander-Gorenstein algebras which are tilted
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    Stephen Zito

    Let Λ be a 1-Auslander-Gorenstein algebra. We give a necessary and sufficient condition for Λ to be a tilted algebra.

    更新日期:2020-03-31
  • Θ-Hilbertianity
    J. Algebra (IF 0.666) Pub Date : 2020-03-31
    S. Fried; D. Haran

    We define Θ-Hilbertianity which generalizes Hilbertianity and show that the absolute Galois group of a countable Θ-Hilbertian PAC field is an appropriate analogue of a free profinite group, thus generalizing a result of Fried-Völklein-Pop.

    更新日期:2020-03-31
  • Core of ideals in one-dimensional Noetherian domains
    J. Algebra (IF 0.666) Pub Date : 2020-03-30
    S. Kabbaj; A. Mimouni

    This paper contributes to the study of the core of ideals in Noetherian rings. We use techniques and objects from multiplicative ideal theory to develop explicit formulas for the core in various classes of one-dimensional Noetherian domains. All results are illustrated with original examples, where we explicitly compute the core.

    更新日期:2020-03-31
  • The maximal rank conjecture for sections of curves
    J. Algebra (IF 0.666) Pub Date : 2020-03-30
    Eric Larson

    Let C⊂Pr be a general curve of genus g embedded via a general linear series of degree d. The Maximal Rank Conjecture asserts that the restriction maps H0(OPr(m))→H0(OC(m)) are of maximal rank; this determines the Hilbert function of C. In this paper, we prove an analogous statement for the union of hyperplane sections of general curves. More specifically, if H⊂Pr is a general hyperplane, and C1,C2

    更新日期:2020-03-31
  • Fuchs' problem for 2-groups
    J. Algebra (IF 0.666) Pub Date : 2020-03-30
    Eric Swartz; Nicholas J. Werner

    Nearly 60 years ago, László Fuchs posed the problem of determining which groups can be realized as the group of units of a commutative ring. To date, the question remains open, although significant progress has been made. Along this line, one could also ask the more general question as to which finite groups can be realized as the group of units of a finite ring. In this paper, we consider the question

    更新日期:2020-03-31
  • On valuation independence and defectless extensions of valued fields
    J. Algebra (IF 0.666) Pub Date : 2020-03-30
    Pablo Cubides Kovacsics; Franz-Viktor Kuhlmann; Anna Rzepka

    In this article we further develop the theory of valuation independence and study its relation with classical notions in valuation theory such as immediate and defectless extensions. We use this general theory to settle two open questions regarding vector space defectless extensions of valued fields. Additionally, we provide a characterization of such extensions within various classes of valued fields

    更新日期:2020-03-30
  • On the simultaneous generation of jets of the adjoint bundles
    J. Algebra (IF 0.666) Pub Date : 2020-03-30
    Junchao Shentu; Yongming Zhang

    In this paper, we investigate the problem of the simultaneous generation of r-jets of the bundle ωX⊗L⊗m, where L is an ample and globally generated line bundle on X. The results work in arbitrary characteristics. A similar problem is studied when X admits singularities.

    更新日期:2020-03-30
  • Almost group theory
    J. Algebra (IF 0.666) Pub Date : 2020-03-20
    Nadja Hempel

    The notions of almost centralizer and almost commutator are introduced and basic properties are established, such as the three subgroup lemma. These notions are used to study M˜c-groups introduced here, that is, groups for which, in every definable sections, every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup

    更新日期:2020-03-21
  • Engel elements in weakly branch groups
    J. Algebra (IF 0.666) Pub Date : 2020-03-19
    Gustavo A. Fernández-Alcober; Marialaura Noce; Gareth M. Tracey

    We study properties of Engel elements in weakly branch groups, lying in the group of automorphisms of a spherically homogeneous rooted tree. More precisely, we prove that the set of bounded left Engel elements is always trivial in weakly branch groups. In the case of branch groups, the existence of non-trivial left Engel elements implies that these are all p-elements and that the group is virtually

    更新日期:2020-03-20
  • Algorithms detecting stability and Morseness for finitely generated groups
    J. Algebra (IF 0.666) Pub Date : 2020-03-16
    Heejoung Kim

    The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group G, Kapovich [31] provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise. In this paper, we give various detection and decidability algorithms

    更新日期:2020-03-16
  • Twisted Lawrence-Krammer representations
    J. Algebra (IF 0.666) Pub Date : 2020-03-12
    Anatole Castella

    Lawrence-Krammer representations are an important family of linear representations of Artin-Tits groups of small type, which are known, under some assumptions on the parameters, to be faithful when the type is spherical (or more generally when they are restricted to the Artin-Tits monoid) and irreducible when the type is connected. Here, we investigate an analogue of these representations — introduced

    更新日期:2020-03-12
  • Glider Brauer-Severi varieties of central simple algebras
    J. Algebra (IF 0.666) Pub Date : 2020-03-06
    Frederik Caenepeel; Fred Van Oystaeyen

    The glider Brauer-Severi variety GBS(A) of a central simple algebra A over a field K is introduced as the set of all irreducible left glider ideals in A for some filtration FA. For fields we deduce that GBS(K) equals R(K)×Z, the product of the Riemann surface of K and Z. For a csa A over K it turns out that GBS(A)=BS(A)×GBS(K), where BS(A) denotes the classical Brauer-Severi variety of A.

    更新日期:2020-03-06
  • Ulrich bundles on the degree six Segre fourfold
    J. Algebra (IF 0.666) Pub Date : 2020-03-03
    F. Malaspina

    We completely characterize the bigraded resolutions of Ulrich bundles of arbitrary rank on the Segre fourfold P2×P2. We characterize the Ulrich bundles V of arbitrary rank on P2×P2 with h1(V⊗Ω⊠Ω)=0 or with h1(V⊗Ω(−1)⊠Ω(−1))=0 or obtained as pullback from P2 and we construct more complicated examples.

    更新日期:2020-03-03
  • Infinite automaton semigroups and groups have infinite orbits
    J. Algebra (IF 0.666) Pub Date : 2020-02-27
    Daniele D'Angeli; Dominik Francoeur; Emanuele Rodaro; Jan Philipp Wächter

    We show that an automaton group or semigroup is infinite if and only if it admits an ω-word (i.e. a right-infinite word) with an infinite orbit, which solves an open problem communicated to us by Ievgen V. Bondarenko. In fact, we prove a generalization of this result, which can be applied to show that finitely generated subgroups and subsemigroups as well as principal left ideals of automaton semigroups

    更新日期:2020-02-28
  • Resolution quiver and cyclic homology criteria for Nakayama algebras
    J. Algebra (IF 0.666) Pub Date : 2020-02-27
    Eric J. Hanson; Kiyoshi Igusa

    If a Nakayama algebra is not cyclic, it has finite global dimension. For a cyclic Nakayama algebra, there are many characterizations of when it has finite global dimension. In [She17], Shen gave such a characterization using Ringel's resolution quiver. In [IZ92], the second author, with Zacharia, gave a cyclic homology characterization for when a monomial relation algebra has finite global dimension

    更新日期:2020-02-28
  • Constructing composition factors for a linear group in polynomial time
    J. Algebra (IF 0.666) Pub Date : 2020-02-25
    Derek Holt; C.R. Leedham-Green; E.A. O'Brien

    We present a Las Vegas polynomial-time algorithm that takes as input a subgroup of GL(d,Fq) and, subject to the existence of certain oracles, determines its composition factors, provided that none of those factors is isomorphic to one of B22(22k+1), F42(22k+1), D43(2k), or G22(32k+1), for any k.

    更新日期:2020-02-25
  • Hom-Lie-Hopf algebras
    J. Algebra (IF 0.666) Pub Date : 2020-02-21
    S. Halıcı; A. Karataş; S. Sütlü

    We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general (α,β)-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are of (α,Id)-type. We show that the universal enveloping Hom-Hopf algebras of a matched pair of Hom-Lie algebras form a matched pair of Hom-Hopf algebras. We observe also that

    更新日期:2020-02-21
  • On complex supersolvable line arrangements
    J. Algebra (IF 0.666) Pub Date : 2020-02-13
    Takuro Abe; Alexandru Dimca

    We show that the number of lines in an m–homogeneous supersolvable line arrangement is upper bounded by 3m−3 and we classify the m–homogeneous supersolvable line arrangements with two modular points up-to lattice-isotopy. We also prove the nonexistence of unexpected curves for supersolvable line arrangements obtained as cones over generic line arrangements, or cones over arbitrary line arrangements

    更新日期:2020-02-20
  • Embedding divisorial schemes into smooth ones
    J. Algebra (IF 0.666) Pub Date : 2020-02-13
    Ferdinando Zanchetta

    Given a quasi-compact and quasi-separated (qcqs) scheme X of finite type over a Noetherian ring R having an ample family of line bundles, we construct a closed embedding of X into a smooth (qcqs) scheme over R having an ample family of line bundles. Such a smooth scheme arises as an open subscheme of the multihomogeneous Proj of a Zn-graded ring.

    更新日期:2020-02-20
  • Minimal ⁎-varieties and minimal supervarieties of polynomial growth
    J. Algebra (IF 0.666) Pub Date : 2020-02-15
    Tatiana Aparecida Gouveia; Rafael Bezerra dos Santos; Ana Cristina Vieira

    By a φ-variety V, we mean a supervariety or a ⁎-variety generated by an associative algebra over a field F of characteristic zero. In this case, we consider its sequence of φ-codimensions cnφ(V) and say that V is minimal of polynomial growth nk if cnφ(V) grows like nk, but any proper φ-subvariety grows like nt with t

    更新日期:2020-02-20
  • Linear differential equations with finite differential Galois group
    J. Algebra (IF 0.666) Pub Date : 2020-02-20
    M. van der Put; C. Sanabria Malagón; J. Top

    For a finite irreducible subgroup H⊂PSL(Cn) and an irreducible, H-invariant curve Z⊂P(Cn) such that C(Z)H=C(t), a standard differential operator Lst∈C(t)[ddt] is constructed. For n=2 this is essentially Klein's work. For n>2 an actual calculation of Lst is done by computing an evaluation of invariants C[X1,…,Xn]H→C(t) and applying a scalar form of a theorem of E. Compoint in a “Procedure”. Also in

    更新日期:2020-02-20
  • Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL4(Z) and Galois representations
    J. Algebra (IF 0.666) Pub Date : 2020-02-20
    Avner Ash; Paul E. Gunnells; Mark McConnell

    We extend the computations in [AGM02], [AGM08], [AGM10] to find the cohomology in degree five of a congruence subgroup of SL4(Z) with coefficients in a field twisted by a nebentype character, along with the action of the Hecke algebra on the cohomology. This is the top cuspidal degree. For each Hecke eigenclass we find, we produce the unique Galois representation that appears to be attached to it.

    更新日期:2020-02-20
  • Discrete and free two-generated subgroups of SL2 over non-archimedean local fields
    J. Algebra (IF 0.666) Pub Date : 2020-02-20
    Matthew J. Conder

    We present a practical algorithm which, given a non-archimedean local field K and any two elements A,B∈SL2(K), determines after finitely many steps whether or not the subgroup 〈A,B〉≤SL2(K) is discrete and free of rank two. This makes use of the Ping Pong Lemma applied to the action of SL2(K) by isometries on its Bruhat-Tits tree. The algorithm itself can also be used for two-generated subgroups of

    更新日期:2020-02-20
  • The word problem of the Brin-Thompson group is coNP-complete
    J. Algebra (IF 0.666) Pub Date : 2020-02-20
    J.C. Birget

    We prove that the word problem of the Brin-Thompson group nV over a finite generating set is coNP-complete for every n≥2. It is known that {nV:n≥1} is an infinite family of infinite, finitely presented, simple groups. We also prove that the word problem of the Thompson group V over a certain infinite set of generators, related to boolean circuits, is coNP-complete.

    更新日期:2020-02-20
  • Central elements in the distribution algebra of a general linear supergroup and supersymmetric elements
    J. Algebra (IF 0.666) Pub Date : 2020-02-20
    František Marko; Alexandr N. Zubkov

    In this paper we investigate the image of the center Z of the distribution algebra Dist(GL(m|n)) of the general linear supergroup over a ground field of positive characteristic under the Harish-Chandra morphism h:Z→Dist(T) obtained by the restriction of the natural map Dist(GL(m|n))→Dist(T). We define supersymmetric elements in Dist(T) and show that each image h(c) for c∈Z is supersymmetric. The central

    更新日期:2020-02-20
  • On the Alperin-McKay conjecture for simple groups of type A
    J. Algebra (IF 0.666) Pub Date : 2020-02-17
    Julian Brough; Britta Späth

    In this paper characters of the normalizer of d-split Levi subgroups in SLn(q) and SUn(q) are parametrized with a particular focus on the Clifford theory between the Levi subgroup and its normalizer. These results are applied to verify the Alperin-McKay conjecture for primes ℓ with ℓ∤6(q2−1) and the Alperin weight conjecture for ℓ-blocks of those quasi-simple groups with abelian defect. The inductive

    更新日期:2020-02-20
  • On the structure of groups with polynomial growth III
    J. Algebra (IF 0.666) Pub Date : 2020-02-17
    Viktor Losert

    We show that a compactly generated locally compact group of polynomial growth having no non-trivial compact normal subgroups can be embedded as a co-compact subgroup into a semidirect product of a connected, simply connected, nilpotent Lie group and a compact group. There is also a uniqueness statement for this extension.

    更新日期:2020-02-20
  • Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
    J. Algebra (IF 0.666) Pub Date : 2020-02-15
    Xing Gao; Li Guo; Yi Zhang

    We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularity structures [10], [19]. This notion is also related to iterated integrals with multiple kernels and solutions of the associative polarized Yang-Baxter equation. Generalizing the natural connection of Rota-Baxter algebras

    更新日期:2020-02-20
  • Connected components of affine primitive permutation groups
    J. Algebra (IF 0.666) Pub Date : 2020-02-13
    Haval M. Mohammed Salih

    For a finite group G, the Hurwitz space Hr,gin(G) is the space of genus g covers of the Riemann sphere with r branch points and the monodromy group G. In this paper, we give a complete list of primitive genus one systems of affine type. That is, we assume that G is a primitive group of affine type. Under this assumption we determine the braid orbits on the suitable Nielsen classes, which is equivalent

    更新日期:2020-02-20
  • Baumann-components of finite groups of characteristic p, reduction theorems
    J. Algebra (IF 0.666) Pub Date : 2020-02-11
    U. Meierfrankenfeld; G. Parmeggiani; B. Stellmacher

    We continue the project started in [8] to describe the structure of the finite groups G of characteristic p in terms of their Baumann components and the conjugacy class Baup(G). The reduction theorem proved in [8] allows to assume that G has a unique Baumann component. In this paper we use this property to determine the isomorphism type of G/Op(G) and the action of G on Ω1(Z(Op(G))). In addition, we

    更新日期:2020-02-12
  • Affine Hecke algebras of type D and generalisations of quiver Hecke algebras
    J. Algebra (IF 0.666) Pub Date : 2020-02-10
    L. Poulain d'Andecy; R. Walker

    We define and study cyclotomic quotients of affine Hecke algebras of type D. We establish an isomorphism between (direct sums of blocks of) these cyclotomic quotients and a generalisation of cyclotomic quiver Hecke algebras which are a family of Z-graded algebras closely related to algebras introduced by Shan, Varagnolo and Vasserot. To achieve this, we first complete the study of cyclotomic quotients

    更新日期:2020-02-10
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