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Quotient toposes of discrete dynamical systems J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-09 Ryuya Hora, Yuhi Kamio
Lawvere's open problem on quotient toposes has been solved for boolean Grothendieck toposes but not for non-boolean toposes. As a simple and non-trivial example of a non-boolean topos, this paper provides a complete classification of the quotient toposes of the topos of discrete dynamical systems, which, in this context, are sets equipped with an endofunction. This paper also offers an order-theoretic
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Waring problem for matrices over finite fields J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Krishna Kishore, Adrian Vasiu, Sailun Zhan
We prove that for all integers , , and , every matrix in is a sum of two kth powers: . We further generalize and refine this result in the cases when both and can be chosen to be invertible, cyclic, or split semisimple, when is coprime to , or when is sufficiently large. We also give a criterion for the Waring problem in terms of stabilizers.
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Ordered locales J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Chris Heunen, Nesta van der Schaaf
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called condition, and the newly defined category of . The adjunction restricts to an equivalence of categories between spatial ordered locales and sober -ordered spaces with open cones.
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Hopf-Galois structures on separable field extensions of degree pq J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-07 Andrew Darlington
In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions is a natural next step. One must consider now the interplay between two Galois groups and , where is the Galois closure of . In this paper, we give a characterisation and enumeration of the Hopf-Galois structures
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Normal subalgebras of a polynomial ring J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-06 R.V. Gurjar, M. Miyanishi
Let be a finitely generated subalgebra of a polynomial ring over the complex field . Assuming that is normal, we clarify the structure of under additional assumptions if . If and is regular, then Spec has an -fibration over or with restrictions on the number of multiple fibers (see Theorem 3). If , we assume that is cofinite, i.e., is a finite -module, and contains a coordinate . Then either is a polynomial
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Quantum traces for [formula omitted]: The case n = 3 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-03-05 Daniel C. Douglas
We generalize Bonahon–Wong's -quantum trace map to the setting of . More precisely, given a non-zero complex parameter , we associate to each isotopy class of framed oriented links in a thickened punctured surface a Laurent polynomial in -deformations of the Fock–Goncharov -coordinates for higher Teichmüller space. This construction depends on a choice of ideal triangulation of the surface . Along
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Powerful 3-Engel groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-28 Iker de las Heras, Marialaura Noce, Gunnar Traustason
In this paper we study finite powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of finite powerful 3-Engel groups and in the subclass of finite powerful metabelian 3-Engel groups.
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Ideal classes of orders in quaternion algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Stefano Marseglia, Harry Smit, John Voight
We provide an algorithm that, given any order in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right -ideals, including the non-invertible ones. The theory is developed for a more general kind of algebras.
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Homological dimensions of Burch ideals, submodules and quotients J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Dipankar Ghosh, Aniruddha Saha
The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is to characterize various local rings in terms of homological invariants of Burch ideals, Burch submodules, or that of the corresponding quotients. Specific applications of our results include the following: Let be a commutative
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Vertex operators for imaginary gl2 subalgebras of the Monster Lie algebra J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich, Maryam Khaqan, Scott H. Murray
The Monster Lie algebra is a quotient of the physical space of the vertex algebra , where is the Moonshine module vertex operator algebra of Frenkel, Lepowsky, and Meurman, and is the vertex algebra corresponding to the rank 2 even unimodular lattice . We construct vertex algebra elements that project to bases for subalgebras of isomorphic to , corresponding to each imaginary simple root, denoted for
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Gröbner geometry for regular nilpotent Hessenberg Schubert cells J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-23 Mike Cummings, Sergio Da Silva, Megumi Harada, Jenna Rajchgot
A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal generators of the defining ideal of a regular nilpotent Hessenberg Schubert cell in the type setting. We show that these minimal generators are a Gröbner basis for an appropriate lexicographic monomial order. As a consequence, we
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On the generating function and growth of the positive singular braid monoid J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-22 A.L. Anisimov, G.A. Kameneva, V.V. Vershinin
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Injectives over Leavitt path algebras of graphs with disjoint cycles J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-21 Gene Abrams, Francesca Mantese, Alberto Tonolo
Let be any field, and let be a finite graph with the property that every vertex in is the base of at most one cycle (i.e., a graph with disjoint cycles). We explicitly construct the injective envelope of each simple left module over the Leavitt path algebra . The main idea girding our construction is that of a “formal power series” extension of modules, thereby developing for all graphs with disjoint
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Vopěnka's principle in ∞-categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-20 Giulio Lo Monaco
In this article, the interplay between Vopěnka's principle, as well as its weaker counterpart, and presentable ∞-categories is studied. Analogous statements, arising after replacing categories with ∞-categories in the original ones, are introduced and compared to these. Further, the attention is focused on the question of to what extent the consequences that (weak) Vopěnka's principle have on the detection
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On the behavior of Massey products under field extension J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-20 Aleksandar Milivojević
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On the obscure axiom for one-sided exact categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-19 Ruben Henrard, Adam-Christiaan van Roosmalen
One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category can be (essentially uniquely) embedded into its exact hull ; this embedding induces a derived equivalence .
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Combinatorial mutations of Gelfand–Tsetlin polytopes, Feigin–Fourier–Littelmann–Vinberg polytopes, and block diagonal matching field polytopes J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-19 Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
The Gelfand-Tsetlin and the Feigin–Fourier–Littelmann–Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bases for highest weight irreducible modules. These polytopes are Newton-Okounkov bodies for the Grassmannian and, in particular, the GT polytope is an example of a string polytope. The polytopes admit a combinatorial description
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Line bundles on G-Bott-Samelson-Demazure-Hansen varieties J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-15 Saurav Bhaumik, Pinakinath Saha
Let be a semi-simple simply connected algebraic group over an algebraically closed field of arbitrary characteristic. Let be a Borel subgroup of containing a maximal torus of . Let be the Weyl group of with respect to . For an arbitrary sequence of simple reflections in , let be the Bott-Samelson-Demazure-Hansen variety (BSDH-variety for short) corresponding to . Let denote the fibre bundle on whose
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Equivalence of v-decomposition matrices for blocks of Ariki-Koike algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-15 Alice Dell'Arciprete
We consider the representation theory of the Ariki-Koike algebra, a -deformation of the group algebra of the complex reflection group . We examine blocks of the Ariki-Koike algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of whose Specht modules belong to a block and those of whose Specht modules belong
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Shapovalov elements of classical and quantum groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-13 Andrey Mudrov
Shapovalov elements of the classical or quantized universal enveloping algebra of a simple Lie algebra are parameterized by a positive root and a positive integer . They relate the highest vector of a reducible Verma module with highest vectors of its submodules. We obtain a factorization of to a product of and calculate as a residue of a matrix element of the inverse Shapovalov form via a generalized
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A Molev-Sagan type formula for double Schubert polynomials J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-12 Matthew J. Samuel
We give a Molev-Sagan type formula for computing the product of two double Schubert polynomials in different sets of coefficient variables where the descents of and satisfy certain conditions that encompass Molev and Sagan's original case and conjecture positivity in the general case. Additionally, we provide a Pieri formula for multiplying an arbitrary double Schubert polynomial by a factorial elementary
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On the degree of varieties of sum of squares J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-10 Andrew Ferguson, Giorgio Ottaviani, Mohab Safey el Din, Ettore Teixeira Turatti
We study the problem of how many different sum of squares decompositions a general polynomial with SOS-rank admits. We show that there is a link between the variety of all SOS-decompositions of and the orthogonal group . We exploit this connection to obtain the dimension of and show that its degree is bounded from below by the degree of . In particular, for we show that is isomorphic to and hence the
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Sum of squares decomposition of positive polynomials with rational coefficients J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-09 Santiago Laplagne
We present an example of a strictly positive polynomial with rational coefficients that can be decomposed as a sum of squares of polynomials over but not over . This answers an open question by C. Scheiderer posed as the second question in . We verify that the example we construct defines a nonsingular projective hypersurface, giving also a positive answer to the third question posed in that section
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On a bijection between a finite group and cyclic group J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-01 Mohsen Amiri
We show that for any finite group of order there exists a bijection from onto the cyclic group such that divides for all . This confirms Problem 18.1 in .
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On some central operators for loop Lie superalgebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-02-01 Sudipta Mukherjee, Santosha Pattanayak, Sachin S. Sharma
Let be either a basic classical Lie superalgebra or over the field of complex numbers . For any associative, commutative, and finitely generated algebra with unity, we consider the loop Lie superalgebra . In , Rao defined a class of central operators for and conjectured that these central operators, which generalizes the classical Gelfand invariants, generate the algebra for . In this article we prove
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Koszul modules of Kac-Moody Lie algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Tymoteusz Chmiel
We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras. We provide a precise criterion for when these modules are of finite length. As an exemplary application we deduce a bound on the dimension of the second graded component for a certain class of graded Kac-Moody Lie algebras. We also provide an exact description of all nilpotent Kac-Moody Koszul modules.
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Naturality of the ∞-categorical enriched Yoneda embedding J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Shay Ben-Moshe
We make Hinich's ∞-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an enriched category. Furthermore, we study a finiteness condition of objects in a tensored category called being atomic, and show that the partial adjunction restricts to a (non-partial)
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A variant of the effective adjunction conjecture with applications J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Zhan Li
We introduce a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.
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On skew partial derivatives and a Hermite-type interpolation problem J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Jonathan Armando Briones Donoso, Andrea Luigi Tironi
Let R:=F[x;σ,δ] be a multivariate skew polynomial ring over a division ring F. In this paper, we introduce the notion of right and left (σ,δ)-partial derivatives of polynomials in R and we prove some of their main properties. As an application of these results, we solve in R a Hermite-type multivariate skew polynomial interpolation problem. The main technical tools and results used here are of constructive
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Semilinear idempotent distributive ℓ-monoids J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Simon Santschi
We prove a representation theorem for totally ordered idempotent monoids via a nested sum construction. Using this representation theorem we obtain a characterization of the subdirectly irreducible members of the variety of semilinear idempotent distributive ℓ-monoids and a proof that its lattice of subvarieties is countably infinite. For the variety of commutative idempotent distributive ℓ-monoids
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Automorphisms of weighted projective hypersurfaces J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-26 Louis Esser
We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we prove in most cases that automorphisms extend to the ambient weighted projective space. We next provide a characterization of when the linear automorphism group is finite and find
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A homotopy coherent nerve for (∞,n)-categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Lyne Moser, Nima Rasekh, Martina Rovelli
In the case of (∞,1)-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of (∞,1)-categories can equivalently be defined as functors of quasi-categories or as simplicially enriched functors out of the homotopy coherent categorifications. In this paper, we
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An analogue of Stone duality via support J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Henning Krause
The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. As an application we indicate some consequences for tensor exact categories
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Magnetic fields on non-singular 2-step nilpotent Lie groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-24 Gabriela P. Ovando, Mauro Subils
This work has a twofold purpose - the existence study of closed 2-forms, known as magnetic fields, on 2-step nilpotent Lie groups and generating examples for the non-singular family. At the Lie algebra level, while the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the existence of closed 2-forms for which the center is
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The magnitude for Nakayama algebras J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Dawei Shen, Yaru Wu
The magnitude for algebras is a generalization of the Euler characteristic. We investigate the magnitude for Nakayama algebras. Using Ringel's resolution quiver, the existence and the value of rational magnitude is given. As a result, we show directly that the finite global dimension criteria for Nakayama algebras of Madsen and the first author are equivalent.
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Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm|n J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-19 B. Feigin, M. Jimbo, E. Mukhin
We define and study the shuffle algebra Shm|n of the quantum toroidal algebra Em|n associated to Lie superalgebra glm|n. We show that Shm|n contains a family of commutative subalgebras Bm|n(s) depending on parameters s=(s1,…,sm+n), ∏isi=1, given by appropriate regularity conditions. We show that Bm|n(s) is a free polynomial algebra and give explicit generators which conjecturally correspond to the
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A certain twisted Jacquet module of GL(6) over a finite field: The rank 2 case J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Kumar Balasubramanian, Himanshi Khurana
Let F be a finite field and G=GL(6,F). In this paper, we explicitly describe the structure of the twisted Jacquet module πN,ψA where A is a rank 2 matrix and π is an irreducible cuspidal representation of G.
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Invariants of non-isolated singularities of hypersurfaces J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Yotam Svoray
In this paper we generalize some results by Siersma, Pellikaan, and de Jong regarding morsifications of singular hypersurfaces whose singular locus is a smooth curve, and present some applications to the study of Yomdin-type isolated singularities. In order to prove these results, we discuss the transversal discriminant of such singularities and how it relates to other algebraic and topological invariants
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Cellular resolutions of monomial ideals and their Artinian reductions J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Sara Faridi, Mohammad D.G. Farrokhi D.G., Roya Ghorbani, Ali Akbar Yazdan Pour
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-complexes? Velasco gave families of examples of monomial ideals that do not have minimal cellular resolutions, but those examples have large minimal generating sets. In this paper, we show that if a monomial ideal has at most
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Indecomposable integrally closed modules of rank 3 over two-dimensional regular local rings J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Futoshi Hayasaka, Vijay Kodiyalam
We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.
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Modified Makar-Limanov and Derksen invariants J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Sergey Gaifullin, Anton Shafarevich
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilpotent derivations with slices and the modified Derksen invariant is the subalgebra generated by these kernels. We prove that the modified Makar-Limanov invariant coincides with the Makar-Limanov invariant if there exists
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Characterizations of tame algebras with separating families of almost cyclic coherent components J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-17 Piotr Malicki
We provide new characterizations of tame algebras with separating families of almost cyclic coherent Auslander–Reiten components in terms of the support of the indecomposable modules, the minimum coordinates of dimension vectors of the indecomposable modules and the values of the Tits quadratic form.
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A refined scissors congruence group and the third homology of SL2 J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-15 Behrooz Mirzaii, Elvis Torres Pérez
There is a natural connection between the third homology of SL2(A) and the refined Bloch group RB(A) of a commutative ring A. In this article we investigate this connection and as the main result we show that if A is a universal GE2-domain such that −1∈A×2, then we have the exact sequenceH3(SM2(A),Z)→H3(SL2(A),Z)→RB(A)→0, where SM2(A) is the group of monomial matrices in SL2(A). Moreover, we show that
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Symbol length in positive characteristic J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-15 Fatma Kader Bingöl
We show that any central simple algebra of exponent p in prime characteristic p that is split by a p-extension of degree pn is Brauer equivalent to a tensor product of 2⋅pn−1−1 cyclic algebras of degree p. If p=2 and n⩾3, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of 5⋅2n−3−1 quaternion algebras. Furthermore, we provide new proofs for some bounds
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Generalized F-signatures of the rings of invariants of finite group schemes J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-15 Mitsuyasu Hashimoto, Fumiya Kobayashi
Let k be a perfect field of prime characteristic p, G a finite group scheme over k, and V a finite-dimensional G-module. Let S=SymV be the symmetric algebra with the standard grading. Let M be a Q-graded S-finite S-free (G,S)-module, and L be its S-reflexive graded (G,S)-submodule. Assume that the action of G on V is small in the sense that there exists some G-stable Zariski closed subset F of V of
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An upper bound on the generic degree of the generalized Verschiebung for rank two stable bundles J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-09 Yuichiro Hoshi, Yasuhiro Wakabayashi
In the present paper, we give an upper bound for the generic degree of the generalized Verschiebung between the moduli spaces of rank two stable bundles with trivial determinant.
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Deformation cohomology for cyclic groups acting on polynomial rings J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-11 Colin M. Lawson, Anne V. Shepler
We examine the Hochschild cohomology governing graded deformations for cyclic groups acting on polynomial rings. We classify the infinitesimal graded deformations of the skew group algebra S⋊G for a cyclic group G acting on a polynomial ring S. This gives all graded deformations of the first order. We are particularly interested in the case when the characteristic of the underlying field divides the
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Morse theory for complexes of groups J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-12 Naya Yerolemou, Vidit Nanda
We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. The key ingredient is a 2-categorical criterion for making acyclic partial matchings on the quotient space compatible with an overlaid complex of groups. We use the discrete flow category of any such compatible matching to build the corresponding Morse complex of groups. Our main result
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Comodule theories in Grothendieck categories and relative Hopf objects J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-08 Mamta Balodi, Abhishek Banerjee, Surjeet Kour
We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category S. We describe when the resulting category of comodules is locally finitely generated, locally noetherian or may be recovered as a coreflective subcategory of the noncommutative base change of a module category. We also introduce the category SHA of relative (A,H)-Hopf modules
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Semisimplicity of some deformations of the subgroup category and the biset category J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-09 Laurence Barker, İsmail Alperen Öğüt
We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star product. For some deformations of the subgroup category, too, we prove a semisimplicity property. The method is to embed the deformations of the biset category into
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Rees Algebras of unit interval determinantal facet ideals J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-04 Ayah Almousa, Kuei-Nuan Lin, Whitney Liske
Using SAGBI basis techniques, we find Gröbner bases for the presentation ideals of the Rees algebras and special fiber rings of unit interval determinantal facet ideals. In particular, we show that unit interval determinantal facet ideals are of fiber type and that their special fiber rings are Koszul. Moreover, their Rees algebras and special fiber rings are normal Cohen-Macaulay domains and have
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The Auslander-Reiten Quiver of Perfect Complexes for a Self-Injective Algebra J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-03 Peter Webb
We consider the homotopy category of perfect complexes for a finite dimensional self-injective algebra over a field, identifying many aspects of perfect complexes according to their position in the Auslander-Reiten quiver. Short complexes lie close to the rim. We characterize the position in the quiver of complexes of lengths 1, 2 and 3, as well as rigid complexes and truncated projective resolutions
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On effective descent V-functors and familial descent morphisms J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-02 Rui Prezado
We study effective descent V-functors for cartesian monoidal categories V with finite limits. This study is carried out via the properties enjoyed by the 2-functor V↦Fam(V), results about effective descent of bilimits of categories, and the fact that the enrichment 2-functor preserves certain bilimits. Since these results rely on an understanding of (effective) descent morphisms in Fam(V), we carefully
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Preservation of Loewy diagrams under exact functors J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-04 Matthew Rupert
We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditions for induction functors associated to simple current extensions of vertex algebras to preserve Loewy diagrams.
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Higher Auslander–Solberg correspondence for exact categories J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-04 Jacob Fjeld Grevstad
We introduce the concept of an n-minimal Auslander–Gorenstein category and n-precluster tilting subcategory. With this, we create an analog of the higher Auslander–Solberg correspondence (Iyama–Solberg 2018) for exact categories. Our approach is based on the recent generalization of the (higher) Auslander correspondence to exact categories (Henrard–Kvamme–Roosmalen 2020, Ebrahimi–Nasr-Isfahani 2021)
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Irreducible Y(gln+1)-module structures on a commutative subalgebra J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-04 Han Dai
The Yangian Y(gln+1) for the general linear Lie algebra gln+1 contains U(gln+1) as a subalgebra. Let h denote the Lie subalgebra of gln+1 generated by trace-zero matrices. We study the category M(Y(gln+1),U(h)) consisting of Y(gln+1)-modules whose restriction to U(h) is free of rank 1. We classify the isomorphism classes of objects in this category and determine the simplicity of these modules. Additionally
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A motivic construction of the de Rham-Witt complex J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-03 Junnosuke Koizumi, Hiroyasu Miyazaki
The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs (X,D) of a variety X and a divisor D. We develop a generalization of this theory where D can be a Q-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor
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Rational certificates of non-negativity on semialgebraic subsets of cylinders J. Pure Appl. Algebra (IF 0.8) Pub Date : 2024-01-02 Gabriela Jeronimo, Daniel Perrucci
Let g1,…,gs∈R[X1,…,Xn,Y] and S={(x¯,y)∈Rn+1|g1(x¯,y)≥0,…,gs(x¯,y)≥0} be a non-empty, possibly unbounded, subset of a cylinder in Rn+1. Let f∈R[X1,…,Xn,Y] be a polynomial which is positive on S. We prove that, under certain additional assumptions, for any non-constant polynomial q∈R[Y] which is positive on R, there is a certificate of the non-negativity of f on S given by a rational function having