• Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
ALBERTO CAVALLO

We introduce a generalization of the Lisca–Ozsváth–Stipsicz–Szabó Legendrian invariant ${\mathfrak L}$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link L in a contact 3-manifold ${(M,\xi)}$ with a diagram D, given by an open book decomposition of ${(M,\xi)}$ adapted to L, and we construct a chain complex ${cCFL^-(D)}$ with

更新日期：2020-08-04
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
ZHIHUA WANG; GONGXIANG LIU; LIBIN LI

Let $\mathcal{C}$ be a fusion category over an algebraically closed field $\mathbb{k}$ of arbitrary characteristic. Two numerical invariants of $\mathcal{C}$ , that is, the Casimir number and the determinant of $\mathcal{C}$ are considered in this paper. These two numbers are both positive integers and admit the property that the Grothendieck algebra $(\mathcal{C})\otimes_{\mathbb{Z}}K$ over any field

更新日期：2020-08-04
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-08-04
T. H. LENAGAN; L. RIGAL

Generalised quantum determinantal rings are the analogue in quantum matrices of Schubert varieties. Maximal orders are the noncommutative version of integrally closed rings. In this paper, we show that generalised quantum determinantal rings are maximal orders. The cornerstone of the proof is a description of generalised quantum determinantal rings, up to a localisation, as skew polynomial extensions

更新日期：2020-08-04
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-29
JORDAN MCMAHON; NICHOLAS J. WILLIAMS

We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective

更新日期：2020-07-29
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-28
HAN YU

In this paper, we follow and extend a group-theoretic method introduced by Greenleaf–Iosevich–Liu–Palsson (GILP) to study finite points configurations spanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove a technical continuity condition in a GILP’s theorem in [Revista Mat. Iberoamer31 (2015), 799–810]. This allows us to extend the Wolff–Erdogan dimension bound for distance sets

更新日期：2020-07-28
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-28
PETER BRUIN; ANTONELLA PERUCCA

Let A be the product of an abelian variety and a torus over a number field K, and let $$m \ge 2$$ be a square-free integer. If $\alpha \in A(K)$ is a point of infinite order, we consider the set of primes $\mathfrak p$ of K such that the reduction $(\alpha \bmod \mathfrak p)$ is well defined and has order coprime to m. This set admits a natural density, which we are able to express as a finite sum

更新日期：2020-07-28
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-23

Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime. These are then used to determine (semi)primeness of certain smash products with quantum affine spaces. This extends Bergen’s work

更新日期：2020-07-23
• Glasg. Math. J. (IF 0.548) Pub Date : 2020-07-10
KUMAR BALASUBRAMANIAN; EKTA TIWARI

Let F be a non-Archimedean local field of characteristic zero. Let G = GL(2, F) and $3\widetildeG = \widetilde{GL}(2,F)$ be the metaplectic group. Let τ be the standard involution on G. A well-known theorem of Gelfand and Kazhdan says that the standard involution takes any irreducible admissible representation of G to its contragredient. In such a case, we say that τ is a dualizing involution. In this

更新日期：2020-07-10
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
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