Publisher: Cambridge University Press   (Total: 386 journals)

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 Glasgow Mathematical JournalJournal Prestige (SJR): 0.604 Number of Followers: 0      Subscription journal ISSN (Print) 0017-0895 - ISSN (Online) 1469-509X Published by Cambridge University Press  [386 journals]
• GMJ volume 62 issue 1 Cover and Front matter
• PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000430
Issue No: Vol. 62, No. 1 (2020)

• GMJ volume 62 issue 1 Cover and Back matter
• PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000442
Issue No: Vol. 62, No. 1 (2020)

• EXTENSIONS OF HILBERTIAN RINGS
• Authors: MOSHE JARDEN; AHARON RAZON
Pages: 1 - 11
Abstract: We generalize known results about Hilbertian fields to Hilbertian rings. For example, let R be a Hilbertian ring (e.g. R is the ring of integers of a number field) with quotient field K and let A be an abelian variety over K. Then, for every extension M of K in K(Ator(Ksep)), the integral closure RM of R in M is Hilbertian.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000496
Issue No: Vol. 62, No. 1 (2020)

• CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS
• Authors: MICHAEL S. WEISS
Pages: 13 - 41
Abstract: Let M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000502
Issue No: Vol. 62, No. 1 (2020)

• A CLASS OF QUASITRIANGULAR GROUP-COGRADED MULTIPLIER HOPF ALGEBRAS
• Authors: TAO YANG; XUAN ZHOU, HAIXING ZHU
Pages: 43 - 57
Abstract: For a multiplier Hopf algebra pairing 〈A,B〉, we construct a class of group-cograded multiplier Hopf algebras D(A,B), generalizing the classical construction of finite dimensional Hopf algebras introduced by Panaite and Staic Mihai [Isr. J. Math. 158 (2007), 349–365]. Furthermore, if the multiplier Hopf algebra pairing admits a canonical multiplier in M(B⊗A) we show the existence of quasitriangular structure on D(A,B). As an application, some special cases and examples are provided.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000514
Issue No: Vol. 62, No. 1 (2020)

• CONCERNING SUMMABLE SZLENK INDEX
• Authors: RYAN MICHAEL CAUSEY
Pages: 59 - 73
Abstract: We generalize the notion of summable Szlenk index from a Banach space to an arbitrary weak*-compact set. We prove that a weak*-compact set has summable Szlenk index if and only if its weak*-closed, absolutely convex hull does. As a consequence, we offer a new, short proof of a result from Draga and Kochanek [J. Funct. Anal. 271 (2016), 642–671] regarding the behavior of summability of the Szlenk index under c0 direct sums. We also use this result to prove that the injective tensor product of two Banach spaces has summable Szlenk index if both spaces do, which answers a question from Draga and Kochanek [Proc. Amer. Math. Soc. 145 (2017), 1685–1698]. As a final consequence of this result, we prove that a separable Banach space has summable Szlenk index if and only if it embeds into a Banach space with an asymptotic c0 finite dimensional decomposition, which generalizes a result from Odell et al. [Q. J. Math. 59, (2008), 85–122]. We also introduce an ideal norm $\mathfrak{s}$ on the class $\mathfrak{S}$ of operators with summable Szlenk index and prove that $(\mathfrak{S}, \mathfrak{s})$ is a Banach ideal. For 1 ⩽ p ⩽ ∞, we prove precise results regarding the summability of the Szlenk index of an ℓp direct sum of a collection of operators.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000526
Issue No: Vol. 62, No. 1 (2020)

• ON NONLOCAL NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN
• Authors: LI MA
Pages: 75 - 84
Abstract: In this paper, we study the existence of positive solutions to a semilinear nonlocal elliptic problem with the fractional α-Laplacian on Rn, 0 < α < n. We show that the problem has infinitely many positive solutions in ${C^\tau}({R^n})\bigcap H_{loc}^{\alpha /2}({R^n})$ . Moreover, each of these solutions tends to some positive constant limit at infinity. We can extend our previous result about sub-elliptic problem to the nonlocal problem on Rn. We also show for α ∊ (0, 2) that in some cases, by the use of Hardy’s inequality, there is a nontrivial non-negative $H_{loc}^{\alpha /2}({R^n})$ weak solution to the problem $${( - \Delta )^{\alpha /2}}u(x) = K(x){u^p} \quad {\rm{ in}} \ {R^n},$$ where K(x) = K(|x|) is a non-negative non-increasing continuous radial function in Rn and p > 1.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000538
Issue No: Vol. 62, No. 1 (2020)

• AN ALGORITHM TO CONSTRUCT THE LE DIAGRAM ASSOCIATED TO A GRASSMANN
NECKLACE
• Authors: SUSAMA AGARWALA; SIÂN FRYER
Pages: 85 - 91
Abstract: Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian Gr≥0(k, n), but they excel at very different tasks: for example, the dimension of a positroid is easily extracted from its Le diagram, while the list of bases of a positroid is far more easily obtained from its Grassmann necklace. Explicit bijections between the two are, therefore, desirable. An algorithm for turning a Le diagram into a Grassmann necklace already exists; in this note, we give the reverse algorithm.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S001708951800054X
Issue No: Vol. 62, No. 1 (2020)

• ON THE NUMBER OF REAL CLASSES IN THE FINITE PROJECTIVE LINEAR AND UNITARY
GROUPS
• Authors: ELENA AMPARO; C. RYAN VINROOT
Pages: 93 - 107
Abstract: We show that for any n and q, the number of real conjugacy classes in $\rm{PGL}(\it{n},\mathbb{F}_q)$ is equal to the number of real conjugacy classes of $\rm{GL}(\it{n},\mathbb{F}_q)$ which are contained in $\rm{SL}(\it{n},\mathbb{F}_q)$ , refining a result of Lehrer [J. Algebra36(2) (1975), 278–286] and extending the result of Gill and Singh [J. Group Theory14(3) (2011), 461–489] that this holds when n is odd or q is even. Further, we show that this quantity is equal to the number of real conjugacy classes in $\rm{PGU}(\it{n},\mathbb{F}_q)$ , and equal to the number of real conjugacy classes of $\rm{U}(\it{n},\mathbb{F}_q)$ which are contained in $\rm{SU}(\it{n},\mathbb{F}_q)$ , refining results of Gow [Linear Algebra Appl.41 (1981), 175–181] and Macdonald [Bull. Austral. Math. Soc.23(1) (1981), 23–48]. We also give a generating function for this common quantity.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000551
Issue No: Vol. 62, No. 1 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\mathbb{H}^{{\it+n}}$ ++++++++++++ ++++++++ ++++&rft.title=Glasgow+Mathematical+Journal&rft.issn=0017-0895&rft.date=2020&rft.volume=62&rft.spage=109&rft.epage=122&rft.aulast=CARRIÃO&rft.aufirst=PAULO&rft.au=PAULO+CESAR+CARRIÃO&rft.au=AUGUSTO+CÉSAR+DOS+REIS+COSTA,+OLIMPIO+HIROSHI+MIYAGAKI&rft_id=info:doi/10.1017/S0017089518000563">A CLASS OF CRITICAL KIRCHHOFF PROBLEM ON THE HYPERBOLIC SPACE
$\mathbb{H}^{{\it n}}$
• Authors: PAULO CESAR CARRIÃO; AUGUSTO CÉSAR DOS REIS COSTA, OLIMPIO HIROSHI MIYAGAKI
Pages: 109 - 122
Abstract: We investigate questions on the existence of nontrivial solution for a class of the critical Kirchhoff-type problems in Hyperbolic space. By the use of the stereographic projection the problem becomes a singular problem on the boundary of the open ball $B_1(0)\subset \mathbb{R}^n$ Combining a version of the Hardy inequality, due to Brezis–Marcus, with the mountain pass theorem due to Ambrosetti–Rabinowitz are used to obtain the nontrivial solution. One of the difficulties is to find a range where the Palais Smale converges, because our equation involves a nonlocal term coming from the Kirchhoff term.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000563
Issue No: Vol. 62, No. 1 (2020)

• LOCAL NEGATIVITY OF SURFACES WITH NON-NEGATIVE KODAIRA DIMENSION AND
TRANSVERSAL CONFIGURATIONS OF CURVES
• Authors: ROBERTO LAFACE; PIOTR POKORA
Pages: 123 - 135
Abstract: We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete intersections $X \subset \mathbb{P}_{\mathbb{C}}^{n + 2}$ of multi-degree d = (d1, …, dn), and we provide a sharp and uniform bound on their H-constants, which only depends on d.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089518000575
Issue No: Vol. 62, No. 1 (2020)

• CHARACTERIZATIONS OF BERGER SPHERES FROM THE VIEWPOINT OF SUBMANIFOLD
THEORY
• Authors: BYUNG HAK KIM; IN-BAE KIM, SADAHIRO MAEDA
Pages: 137 - 145
Abstract: In this paper, Berger spheres are regarded as geodesic spheres with sufficiently big radii in a complex projective space. We characterize such real hypersurfaces by investigating their geodesics and contact structures from the viewpoint of submanifold theory.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000016
Issue No: Vol. 62, No. 1 (2020)

• ORIENTED FLIP GRAPHS, NONCROSSING TREE PARTITIONS, AND REPRESENTATION
THEORY OF TILING ALGEBRAS
• Authors: ALEXANDER GARVER; THOMAS MCCONVILLE
Pages: 147 - 182
Abstract: The purpose of this paper is to understand lattices of certain subcategories in module categories of representation-finite gentle algebras called tiling algebras, as introduced by Coelho Simões and Parsons. We present combinatorial models for torsion pairs and wide subcategories in the module category of tiling algebras. Our models use the oriented flip graphs and noncrossing tree partitions, previously introduced by the authors, and a description of the extension spaces between indecomposable modules over tiling algebras. In addition, we classify two-term simple-minded collections in bounded derived categories of tiling algebras. As a consequence, we obtain a characterization of c-matrices for any quiver mutation-equivalent to a type A Dynkin quiver.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000028
Issue No: Vol. 62, No. 1 (2020)

• p-SUBGROUPS+IN+SIMPLE+LOCALLY+FINITE+GROUPS&rft.title=Glasgow+Mathematical+Journal&rft.issn=0017-0895&rft.date=2020&rft.volume=62&rft.spage=183&rft.epage=186&rft.aulast=ERSOY&rft.aufirst=KIVANÇ&rft.au=KIVANÇ+ERSOY&rft_id=info:doi/10.1017/S001708951900003X">CENTRALIZERS OF p-SUBGROUPS IN SIMPLE LOCALLY
FINITE GROUPS
• Authors: KIVANÇ ERSOY
Pages: 183 - 186
Abstract: In Ersoy et al. [J. Algebra481 (2017), 1–11], we have proved that if G is a locally finite group with an elementary abelian p-subgroup A of order strictly greater than p2 such that CG(A) is Chernikov and for every non-identity α ∈ A the centralizer CG(α) does not involve an infinite simple group, then G is almost locally soluble. This result is a consequence of another result proved in Ersoy et al. [J. Algebra481 (2017), 1–11], namely: if G is a simple locally finite group with an elementary abelian group A of automorphisms acting on it such that the order of A is greater than p2, the centralizer CG(A) is Chernikov and for every non-identity α ∈ A the set of fixed points CG(α) does not involve an infinite simple groups then G is finite. In this paper, we improve this result about simple locally finite groups: Indeed, suppose that G is a simple locally finite group, consider a finite non-abelian subgroup P of automorphisms of exponent p such that the centralizer CG(P) is Chernikov and for every non-identity α ∈ P the set of fixed points CG(α) does not involve an infinite simple group. We prove that if Aut(G) has such a subgroup, then G ≅PSLp(k) where char k ≠ p and P has a subgroup Q of order p2 such that CG(P) = Q.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S001708951900003X
Issue No: Vol. 62, No. 1 (2020)

• NONNEGATIVE MULTIPLICATIVE FUNCTIONS ON SIFTED SETS, AND THE SQUARE ROOTS
OF −1 MODULO SHIFTED PRIMES
• Authors: PAUL POLLACK
Pages: 187 - 199
Abstract: An oft-cited result of Peter Shiu bounds the mean value of a nonnegative multiplicative function over a coprime arithmetic progression. We prove a variant where the arithmetic progression is replaced by a sifted set. As an application, we show that the normalized square roots of −1 (mod m) are equidistributed (mod 1) as m runs through the shifted primes q − 1.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000041
Issue No: Vol. 62, No. 1 (2020)

• C*-ALGEBRAS&rft.title=Glasgow+Mathematical+Journal&rft.issn=0017-0895&rft.date=2020&rft.volume=62&rft.spage=201&rft.epage=231&rft.aulast=GABE&rft.aufirst=JAMES&rft.au=JAMES+GABE&rft.au=EFREN+RUIZ&rft_id=info:doi/10.1017/S0017089519000053">THE UNITAL EXT-GROUPS AND CLASSIFICATION OF        class="italic">C*-ALGEBRAS
• Authors: JAMES GABE; EFREN RUIZ
Pages: 201 - 231
Abstract: The semigroups of unital extensions of separable C*-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C*-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000053
Issue No: Vol. 62, No. 1 (2020)

• EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND
COHOMOLOGY
• Authors: PATRIK NYSTEDT; JOHAN ÖINERT, HÉCTOR PINEDO
Pages: 233 - 259
Abstract: We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S0017089519000065
Issue No: Vol. 62, No. 1 (2020)

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