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  • CLOSED IDEALS AND LIE IDEALS OF MINIMAL TENSOR PRODUCT OF CERTAIN C*-ALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-03
    BHARAT TALWAR; RANJANA JAIN

    For a locally compact Hausdorff space X and a C*-algebra A with only finitely many closed ideals, we discuss a characterization of closed ideals of C0(X,A) in terms of closed ideals of A and a class of closed subspaces of X. We further use this result to prove that a closed ideal of C0(X)⊗minA is a finite sum of product ideals. We also establish that for a unital C*-algebra A, C0(X,A) has the centre-quotient

    更新日期:2020-07-03
  • CYCLIC BRANCHED COVERINGS OF BRIESKORN SPHERES BOUNDING ACYCLIC 4-MANIFOLDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-03
    NIMA ANVARI; IAN HAMBLETON

    We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic 4-manifold with boundary a related Brieskorn homology sphere. We briefly discuss well-known invariants of homology spheres that obstruct acyclic bounding 4-manifolds and then use

    更新日期:2020-07-03
  • POTENTIAL ALGEBRAS WITH FEW GENERATORS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-01
    NATALIA IYUDU; STANISLAV SHKARIN

    We give a complete description of quadratic twisted potential algebras on three generators as well as cubic twisted potential algebras on two generators up to graded algebra isomorphisms under the assumption that the ground field is algebraically closed and has characteristic other than 2 or 3.

    更新日期:2020-07-01
  • A FAST ALGORITHM FOR CALCULATING S-INVARIANTS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-29
    DIRK SCHÜTZ

    We use the divide-and-conquer and scanning algorithms for calculating Khovanov cohomology directly on the Lee- or Bar-Natan deformations of the Khovanov complex to give an alternative way to compute Rasmussen s-invariants of knots. By disregarding generators away from homological degree 0, we can considerably improve the efficiency of the algorithm. With a slight modification, we can also apply it

    更新日期:2020-06-29
  • DISTAL ACTIONS OF AUTOMORPHISMS OF NILPOTENT GROUPS G ON SUBG AND APPLICATIONS TO LATTICES IN LIE GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-23
    RAJDIP PALIT; RIDDHI SHAH

    For a locally compact group G, we study the distality of the action of automorphisms T of G on SubG, the compact space of closed subgroups of G endowed with the Chabauty topology. For a certain class of discrete groups G, we show that T acts distally on SubG if and only if Tn is the identity map for some $n\in\mathbb N$ . As an application, we get that for a T-invariant lattice Γ in a simply connected

    更新日期:2020-06-23
  • NONHYPERELLIPTIC FIBRATIONS OF GENUS 4 WITH NONSURJECTIVE MULTIPLICATION MAP
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-06-15
    TOMOKUNI TAKAHASHI

    We prove some numerical inequality for the Horikawa indices for Eisenbud–Harris special nonhyperelliptic fibrations of genus 4 on algebraic surfaces under the assumption that the multiplication map of the fibration is not surjective. Furthermore, we prove that the inequality is best possible by constructing the examples satisfying the equality.

    更新日期:2020-06-15
  • DETECTING STEINER AND LINEAR ISOMETRIES OPERADS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-19
    JONATHAN RUBIN

    We study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When G is a finite abelian group, we prove that a G-indexing system is realized by a Steiner operad if and only if it is generated by cyclic G-orbits. When G is a finite cyclic group, whose order is either a prime power or a product of two distinct primes greater than 3, we prove that a G-indexing system

    更新日期:2020-05-19
  • ISOTOPY AND HOMEOMORPHISM OF CLOSED SURFACE BRAIDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-15
    MARK GRANT; AGATA SIENICKA

    The closure of a braid in a closed orientable surface Ʃ is a link in Ʃ × S1. We classify such closed surface braids up to isotopy and homeomorphism (with a small indeterminacy for isotopy of closed sphere braids), algebraically in terms of the surface braid group. We find that in positive genus, braids close to isotopic links if and only if they are conjugate, and close to homeomorphic links if and

    更新日期:2020-05-15
  • A NOTE ON CHAINS AND BOUNDING PAIRS OF DEHN TWISTS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-15
    FERIHE ATALAN

    Let $N_g^k$ be a nonorientable surface of genus g with k punctures. In the first part of this note, after introducing preliminary materials, we will give criteria for a chain of Dehn twists to bound a disc. Then, we will show that automorphisms of the mapping class groups map disc bounding chains of Dehn twists to such chains. In the second part of the note, we will introduce bounding pairs of Dehn

    更新日期:2020-05-15
  • AN EXTENSION OF A RESULT OF ERDŐS AND ZAREMBA
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-13
    MICHEL JEAN GEORGES WEBER

    Erdös and Zaremba showed that $ \limsup_{n\to \infty} \frac{\Phi(n)}{(\log\log n)^2}=e^\gamma$ , γ being Euler’s constant, where $\Phi(n)=\sum_{d|n} \frac{\log d}{d}$ .

    更新日期:2020-05-13
  • PRIMITIVE RECURSIVE DECIDABILITY FOR THE RING OF INTEGERS OF THE COMPOSITUM OF ALL SYMMETRIC EXTENSIONS OF ℚ
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-08
    MOSHE JARDEN; AHARON RAZON

    Let ℚsymm be the compositum of all symmetric extensions of ℚ, i.e., the finite Galois extensions with Galois group isomorphic to Sn for some positive integer n, and let ℤsymm be the ring of integers inside ℚsymm. Then, TH(ℤsymm) is primitive recursively decidable.

    更新日期:2020-05-08
  • NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-05-07
    IGNACIO F. RÚA

    Symplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$

    更新日期:2020-05-07
  • HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-27
    MICHAEL J. CRABB; JOHN DUNCAN; COLIN M. McGREGOR

    We investigate the real space H of Hermitian matrices in $M_n(\mathbb{C})$ with respect to norms on $\mathbb{C}^n$ . For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9–31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of

    更新日期:2020-04-27
  • ON SOME QUESTIONS OF PARTITIO NUMERORUM: TRES CUBI
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-21
    R. C. VAUGHAN

    This paper is concerned with the function r3(n), the number of representations of n as the sum of at most three positive cubes, $$r_3(n) = {\mathrm{card}}\{\mathbf m\in\mathbb Z^3: m_1^3+m_2^3+m_3^3=n, m_j\ge1\}.$$ , Our understanding of this function is surprisingly poor, and we examine various averages of it. In particular $${\sum_{m=1}^nr_3(m),\,\sum_{m=1}^nr_3(m)^2}$$ and $${\sum_{\substack{ n\le

    更新日期:2020-04-21
  • BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-20
    GENQIANG LIU; YANG LI

    In 1996, a q-deformation of the universal enveloping algebra of the Schrödinger Lie algebra was introduced in Dobrev et al. [J. Phys. A 29 (1996) 5909–5918.]. This algebra is called the quantum Schrödinger algebra. In this paper, we study the Bernstein-Gelfand-Gelfand (BGG) category $\mathcal{O}$ for the quantum Schrödinger algebra $U_q(\mathfrak{s})$ , where q is a nonzero complex number which is

    更新日期:2020-04-20
  • ANNIHILATOR-STABILITY AND TWO QUESTIONS OF NICHOLSON
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-07
    GUOLI XIA; YIQIANG ZHOU

    An element a in a ring R is left annihilator-stable (or left AS) if, whenever $Ra+{\rm l}(b)=R$ with $b\in R$ , $a-u\in {\rm l}(b)$ for a unit u in R, and the ring R is a left AS ring if each of its elements is left AS. In this paper, we show that the left AS elements in a ring form a multiplicatively closed set, giving an affirmative answer to a question of Nicholson [J. Pure Appl. Alg.221 (2017)

    更新日期:2020-04-07
  • ON THE EIGENVALUES AND THE NODAL POINTS OF THE EIGENFUNCTIONS OF SOME EIGENVALUE PROBLEMS WITH EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-07
    CHI-HUA CHAN; PO-CHUN HUANG

    Consider the following two eigenvalue problems: (0.1) \begin{cases}\label{eqn:1abs}y"(x)+[\lambda^2-q(x)]y(x)=0, 0 \leq x \leq \pi,\\[3pt] y(0)=0, ay'(\pi)+\lambda y(\pi)=0, \end{cases} and (0.2) \begin{cases} z"(x)+[\mu^2-q(x)]z(x)=0, 0 \leq x \leq \pi,\\[3pt] z'(0)=0, az'(\pi)+\mu z(\pi)=0, \end{cases}

    更新日期:2020-04-07
  • FOUR-MANIFOLDS WITH POSITIVE CURVATURE
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-04-06
    R. DIÓGENES; E. RIBEIRO; E. RUFINO

    In this note, we prove that a four-dimensional compact oriented half-conformally flat Riemannian manifold M4 is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2}$ , provided that the sectional curvatures all lie in the interval $\left[ {{{3\sqrt {3 - 5} } \over 4}, 1} \right]$ In addition, we use the notion of biorthogonal (sectional) curvature to obtain a pinching condition which guarantees

    更新日期:2020-04-06
  • (WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-16
    ULRICH KRÄHMER; LUCIA ROTHERAY

    Incidence coalgebras of categories in the sense of Joni and Rota are studied, specifically cases where a monoidal product on the category turns these into (weak) bialgebras. The overlap with the theory of combinatorial Hopf algebras and that of Hopf quivers is discussed, and examples including trees, skew shapes, Milner’s bigraphs and crossed modules are considered.

    更新日期:2020-03-16
  • FRACTIONAL SCHRÖDINGER–POISSON SYSTEM WITH SINGULARITY: EXISTENCE, UNIQUENESS, AND ASYMPTOTIC BEHAVIOR
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12
    SHENGBIN YU; JIANQING CHEN

    In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*}

    更新日期:2020-03-12
  • WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-03-12
    BOUALEM BENSEBAA; ABBAS MOVAHHEDI; ALAIN SALINIER

    It is proven that, for a wide range of integers s (2 < s < p − 2), the existence of a single wildly ramified odd prime l ≠ p leads to either the alternating group or the full symmetric group as Galois group of any irreducible trinomial Xp + aXs + b of prime degree p.

    更新日期:2020-03-12
  • ON THE σ-NILPOTENT NORM AND THE σ-NILPOTENT LENGTH OF A FINITE GROUP
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-27
    BIN HU; JIANHONG HUANG; ALEXANDER N. SKIBA

    Let G be a finite group and σ = {σi| i ∈ I} some partition of the set of all primes $\Bbb{P}$ . Then G is said to be: σ-primary if G is a σi-group for some i; σ-nilpotent if G = G1× … × Gt for some σ-primary groups G1, … , Gt; σ-soluble if every chief factor of G is σ-primary. We use $G^{{\mathfrak{N}}_{\sigma}}$ to denote the σ-nilpotent residual of G, that is, the intersection of all normal subgroups

    更新日期:2020-02-27
  • FINITENESS OF TOPOLOGICAL ENTROPY FOR LOCALLY COMPACT ABELIAN GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-26
    DIKRAN DIKRANJAN; ANNA GIORDANO BRUNO; FRANCESCO G. RUSSO

    We study the locally compact abelian groups in the class ${\mathfrak E_{ \lt \infty }}$ , that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$ , that is, having all continuous endomorphisms with vanishing topological entropy. We discuss the reduction of the problem to the case of periodic locally compact abelian groups, and then to locally

    更新日期:2020-02-26
  • GENERALIZED FINITE POLYLOGARITHMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-19
    MARINA AVITABILE; SANDRO MATTAREI

    We introduce a generalization ${\rm{\pounds}}_d^{(\alpha)}(X)$ of the finite polylogarithms ${\rm{\pounds}}_d^{(0)}(X) = {{\rm{\pounds}}_d}(X) = \sum\nolimits_{k = 1}^{p - 1} {X^k}/{k^d}$ , in characteristic p, which depends on a parameter α. The special case ${\rm{\pounds}}_1^{(\alpha)}(X)$ was previously investigated by the authors as the inverse, in an appropriate sense, of a parametrized generalization

    更新日期:2020-02-19
  • GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-02-03
    DUNCAN MCCOY

    For p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large

    更新日期:2020-02-03
  • POWERS OF THE MAXIMAL IDEAL AND VANISHING OF (CO)HOMOLOGY
    Glasg. Math. J. (IF 0.548) Pub Date : 2020-01-10
    OLGUR CELIKBAS; RYO TAKAHASHI

    We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid and strongly rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion condition of a long-standing conjecture of Huneke and Wiegand.

    更新日期:2020-01-10
  • ON FINITE-BY-NILPOTENT GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-20
    ELOISA DETOMI; GURAM DONADZE; MARTA MORIGI; PAVEL SHUMYATSKY

    Let γn = [x1,…,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that $|{g^{{X_n}}}| \le m$ for each g ∈ G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.

    更新日期:2019-12-20
  • THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-12
    LEONID CHAICHENETS; NIKOLAOS PATTAKOS

    We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$ , where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities.

    更新日期:2019-12-12
  • HOMOLOGY THEORIES FOR COMPLEXES BASED ON FLATS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-12-02
    LI LIANG

    In this paper, we introduce and study the Gorenstein relative homology theory for unbounded complexes of modules over arbitrary associative rings, which is defined using special Gorenstein flat precovers. We compare the Gorenstein relative homology to the Tate/unbounded homology and get some results that improve the known ones.

    更新日期:2019-12-02
  • HOW A NONASSOCIATIVE ALGEBRA REFLECTS THE PROPERTIES OF A SKEW POLYNOMIAL
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-11-26
    C. BROWN; S. PUMPLÜN

    Let D be a unital associative division ring and D[t, σ, δ] be a skew polynomial ring, where σ is an endomorphism of D and δ a left σ-derivation. For each f ϵ D[t, σ, δ] of degree m > 1 with a unit as leading coefficient, there exists a unital nonassociative algebra whose behaviour reflects the properties of f. These algebras yield canonical examples of right division algebras when f is irreducible

    更新日期:2019-11-26
  • OPERADIC APPROACH TO COHOMOLOGY OF ASSOCIATIVE TRIPLE AND N-TUPLE SYSTEMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-11-14
    FATEMEH BAGHERZADEH; MURRAY BREMNER

    The cup product in the cohomology of algebras over quadratic operads has been studied in the general setting of Koszul duality for operads. We study the cup product on the cohomology of n-ary totally associative algebras with an operation of even (homological) degree. This cup product endows the cohomology with the structure of an n-ary partially associative algebra with an operation of even or odd

    更新日期:2019-11-14
  • (t, ℓ)-STABILITY AND COHERENT SYSTEMS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-09
    L. BRAMBILA-PAZ; O. MATA-GUTIÉRREZ

    Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.

    更新日期:2019-10-09
  • ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-07
    FLORIAN BOUYER

    In [5], Eklund showed that a general (ℤ/2ℤ)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (ℤ/2ℤ)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.

    更新日期:2019-10-07
  • OPEN BOOKS FOR CLOSED NON-ORIENTABLE 3–MANIFOLDS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-07
    ABHIJEET GHANWAT; SUHAS PANDIT; A SELVAKUMAR

    In this note, we give a new proof of the existence of an open book decomposition for a closed non-orientable 3–manifold. This open book decomposition is analogous to a planar open book decomposition for a closed orientable 3–manifold. More precisely, in this note, we give an open book decomposition of a given closed non-orientable 3–manifold with the pages punctured Möbius bands. We also give an algorithm

    更新日期:2019-10-07
  • DIVISION SUDOKUS: INVARIANTS, ENUMERATION, AND MULTIPLE PARTITIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-02
    ALEŠ DRÁPAL; PETR VOJTĚCHOVSKÝ

    A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich

    更新日期:2019-10-02
  • POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-10-02
    DAVID KYED; HENRIK DENSING PETERSEN

    We introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly

    更新日期:2019-10-02
  • QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-30
    QILIAN ZHENG; JIAQUN WEI

    The notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$ . Then the quotient category ${\cal Z}/{\cal D}$ carries naturally an (n + 2) -angulated structure whenever $ ({\cal Z},{\cal Z}) $ forms a ${\cal D} \subseteq {\cal Z}$ -mutation pair and ${\cal Z}$ is extension-closed

    更新日期:2019-09-30
  • QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-27
    PAWEŁ JÓZIAK

    We answer a question of Skalski and Sołan (2016) about inner faithfulness of the Curran’s map of extending a quantum increasing sequence to a quantum permutation. Roughly speaking, we find a inductive setting in which the inner faithfulness of Curran’s map can be boiled down to inner faithfulness of similar map for smaller algebras and then rely on inductive generation result for quantum permutation

    更新日期:2019-09-27
  • BANACH ALGEBRAS OF VECTOR-VALUED FUNCTIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-09-06
    AZADEH NIKOU; ANTHONY G. O’FARRELL

    We correct an error in our paper published in volume 56 of this journal.

    更新日期:2019-09-06
  • COALTERNATIVE COALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-08-20
    HELENA ALBUQUERQUE; ELISABETE BARREIRO; JOSÉ M. SÁNCHEZ; CARLOS SONEIRA CALVO

    In this paper, we define a Cayley–Dickson process for k-coalgebras proving some results that describe the properties of the final coalgebra, knowing the properties of the initial one. Namely, after applying the Cayley–Dickson process for k-coalgebras to a coassociative coalgebra, we obtain a coalternative one. Moreover, the first coalgebra is cocommutative if and only if the final coalgebra is coassociative

    更新日期:2019-08-20
  • BIFURCATION PROPERTIES FOR A CLASS OF CHOQUARD EQUATION IN WHOLE R3 - ERRATUM
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-08-14
    CLAUDIANOR O. ALVES; ROMILDO N. DE LIMA; ALÂNNIO B. NÓBREGA

    This paper concerns the study of some bifurcation properties for the following class of Choquard-type equations: (P) $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u = \lambda f(x)\left[ {u + \left( {{I_\alpha }*f( \cdot )H(u)} \right)h(u)} \right],{\rm{ in }} \ {{\mathbb{R}}^3},}\\ {{{\lim }_{|x| \to \infty }}u(x) = 0,\quad u(x) > 0,\quad x \in {{\mathbb{R}}^3},\quad u \in {D^{1,2}}({{\mathbb{R}}^3})

    更新日期:2019-08-14
  • THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-07-29
    VOLODYMYR V. BAVULA; TAO LU

    Let 𝔟 be the Borel subalgebra of the Lie algebra 𝔰𝔩2 and V2 be the simple two-dimensional 𝔰𝔩2-module. For the universal enveloping algebra $\[{\cal A}: = U(\gb \ltimes {V_2})\]$ of the semi-direct product 𝔟⋉V2 of Lie algebras, the prime, primitive and maximal spectra are classified. Please approve edit to the sentence “The sets of completely prime…”.The sets of completely prime ideals of $\[{\cal

    更新日期:2019-07-29
  • BIFURCATION PROPERTIES FOR A CLASS OF CHOQUARD EQUATION IN WHOLE ℝ3†
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-07-11
    CLAUDIANOR O. ALVES; ROMILDO N. DE LIMA; ALÂNNIO B. NÓBREGA

    This paper concerns the study of some bifurcation properties for the following class of Choquard-type equations: (P) $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u = \lambda f(x)\left[ {u + \left( {{I_\alpha }*f( \cdot )H(u)} \right)h(u)} \right],{\rm{ in }} \ {{\mathbb{R}}^3},}\\ {{{\lim }_{|x| \to \infty }}u(x) = 0,\quad u(x) > 0,\quad x \in {{\mathbb{R}}^3},\quad u \in {D^{1,2}}({{\mathbb{R}}^3})

    更新日期:2019-07-11
  • α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-07-03
    BENEDIKT HURLE; ABDENACER MAKHLOUF

    The purpose of this paper is to define an α-type cohomology, which we call α-type Chevalley–Eilenberg cohomology, for Hom-Lie algebras. We relate it to the known Chevalley–Eilenberg cohomology and provide explicit computations for some examples. Moreover, using this cohomology, we study formal deformations of Hom-Lie algebras, where the bracket as well as the structure map α are deformed. Furthermore

    更新日期:2019-07-03
  • LOCALIZATIONS OF THE HEARTS OF COTORSION PAIRS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-07-03
    YU LIU

    In this article, we study localizations of hearts of cotorsion pairs ( $\mathcal{U}, \mathcal{V}$ ) where $\mathcal{U}$ is rigid on an extriangulated category $\mathcal{B}$ . The hearts of such cotorsion pairs are equivalent to the functor categories over the stable category of $\mathcal{U}$ ( $\bmod \underline{\mathcal{U}}$ ). Inspired by Marsh and Palu (Nagoya Math. J.225(2017), 64–99), we consider

    更新日期:2019-07-03
  • CLASSIFICATION OF FINITE GROUPS VIA THEIR BREADTH
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-27
    HERMANN HEINEKEN; FRANCESCO G. RUSSO

    Let k be a divisor of a finite group G and Lk(G) = {x ∈ G | xk =1}. Frobenius proved that the number |Lk(G)| is always divisible by k. The following inverse problem is considered: for a given integer n, find all groups G such that max{k-1|Lk(G)| | k ∈ Div(G)} = n, where Div(G) denotes the set of all divisors of |G|. A procedure beginning with (in a sense) minimal members and deducing the remaining

    更新日期:2019-06-27
  • ON THE RECOGNITION OF RIGHT-ANGLED ARTIN GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-19
    MARTIN R. BRIDSON

    There does not exist an algorithm that can determine whether or not a group presented by commutators is a right-angled Artin group.

    更新日期:2019-06-19
  • NAKAYAMA AUTOMORPHISMS OF ORE EXTENSIONS OVER POLYNOMIAL ALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-17
    LIYU LIU; WEN MA

    Nakayama automorphisms play an important role in the fields of noncommutative algebraic geometry and noncommutative invariant theory. However, their computations are not easy in general. We compute the Nakayama automorphism ν of an Ore extension R[x; σ, δ] over a polynomial algebra R in n variables for an arbitrary n. The formula of ν is obtained explicitly. When σ is not the identity map, the invariant

    更新日期:2019-06-17
  • DECOMPOSING THE TUBE CATEGORY
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-17
    LEONARD HARDIMAN; ALASTAIR KING

    The tube category of a modular tensor category is a variant of the tube algebra, first introduced by Ocneanu. As a category, it can be decomposed in two different, but related, senses. Firstly, via the Yoneda embedding, the Hom spaces decompose into summands factoring through irreducible functors, in a manner analogous to decomposing an algebra as a sum of matrix algebras. We describe these summands

    更新日期:2019-06-17
  • JORDAN BIMODULES OVER THE SUPERALGEBRA M1|1
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-14
    CONSUELO MARTÍNEZ; IVAN SHESTAKOV

    Let F be a field of characteristic different of 2 and let M1|1(F)(+) denote the Jordan superalgebra of 2 × 2 matrices over the field F. The aim of this paper is to classify irreducible (unital and one-sided) Jordan bimodules over the Jordan superalgebra M1|1(F)(+).

    更新日期:2019-06-14
  • ON LOCAL FIELDS GENERATED BY DIVISION VALUES OF FORMAL DRINFELD MODULES
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-14
    HASSAN OUKHABA

    In this paper, we study some aspects of the local fields generated by division values of formal Drinfeld modules.

    更新日期:2019-06-14
  • CONVEXITY OF PARAMETER EXTENSIONS OF SOME RELATIVE OPERATOR ENTROPIES WITH A PERSPECTIVE APPROACH
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-06-06
    ISMAIL NIKOUFAR

    In this paper, we introduce two notions of a relative operator (α, β)-entropy and a Tsallis relative operator (α, β)-entropy as two parameter extensions of the relative operator entropy and the Tsallis relative operator entropy. We apply a perspective approach to prove the joint convexity or concavity of these new notions, under certain conditions concerning α and β. Indeed, we give the parametric

    更新日期:2019-06-06
  • DIVIDED POWER ALGEBRAS OVER AN OPERAD
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-27
    SACHA IKONICOFF

    The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We describe these polynomial operations in two different ways: one way uses invariant elements under the action of the symmetric group and the other coinvariant elements

    更新日期:2019-05-27
  • ON REPRESENTATIONS OF SYMMETRIC LEIBNIZ ALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-23
    SAÏD BENAYADI

    We give a new and useful approach to study the representations of symmetric Leibniz algebras. Using this approach, we obtain some results on the representations of these algebras.

    更新日期:2019-05-23
  • CLASS NUMBER FORMULA FOR DIHEDRAL EXTENSIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-21
    LUCA CAPUTO; FILIPPO A. E. NUCCIO MORTARINO MAJNO DI CAPRIGLIO

    We give an algebraic proof of a class number formula for dihedral extensions of number fields of degree 2q, where q is any odd integer. Our formula expresses the ratio of class numbers as a ratio of orders of cohomology groups of units and allows one to recover similar formulas which have appeared in the literature. As a corollary of our main result, we obtain explicit bounds on the (finitely many)

    更新日期:2019-05-21
  • CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-07
    ISABEL CUNHA; ALBERTO ELDUQUE

    The exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

    更新日期:2019-05-07
  • FLAT RING EPIMORPHISMS OF COUNTABLE TYPE
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-07
    LEONID POSITSELSKI

    Let R→U be an associative ring epimorphism such that U is a flat left R-module. Assume that the related Gabriel topology $\mathbb{G}$ of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1. Furthermore, the abelian category of left contramodules over the completion of R at $\mathbb{G}$ fully faithfully embeds into the Geigle–Lenzing right

    更新日期:2019-05-07
  • JSJ DECOMPOSITIONS OF DOUBLES OF FREE GROUPS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-05-02
    SIMON HEIL

    We classify all possible JSJ decompositions of doubles of free groups of rank two, and we also compute the Makanin–Razborov diagram of a particular double of a free group and deduce that in general limit groups are not freely subgroup separable.

    更新日期:2019-05-02
  • PARABOLIC SUBROOT SYSTEMS AND THEIR APPLICATIONS
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-04-30
    JOHN M. BURNS; MOHAMMAD A. MAKROONI

    In this note we consider parabolic subroot systems of a complex simple Lie Algebra. We describe root theoretic data of the subroot systems in terms of that of the root system and we give a selection of applications of our results to the study of generalized flag manifolds.

    更新日期:2019-04-30
  • SOLVABLE CROSSED PRODUCT ALGEBRAS REVISITED
    Glasg. Math. J. (IF 0.548) Pub Date : 2019-04-08
    CHRISTIAN BROWN; SUSANNE PUMPLÜN

    For any central simple algebra over a field F which contains a maximal subfield M with non-trivial automorphism group G = AutF(M), G is solvable if and only if the algebra contains a finite chain of subalgebras which are generalized cyclic algebras over their centers (field extensions of F) satisfying certain conditions. These subalgebras are related to a normal subseries of G. A crossed product algebra

    更新日期:2019-04-08
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