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Small groups of finite Morley rank with a supertight automorphism J. Algebra (IF 0.9) Pub Date : 2024-03-12 Ulla Karhumäki, Pınar Uğurlu Kowalski
Let be an infinite simple group of finite Morley rank and of Prüfer 2-rank 1 which admits a supertight automorphism such that the fixed-point subgroup is pseudofinite for all integers . The main result of this paper is the identification of with for some algebraically closed field of characteristic ≠2.
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Symplectic structures, product structures and complex structures on Leibniz algebras J. Algebra (IF 0.9) Pub Date : 2024-03-08 Rong Tang, Nanyan Xu, Yunhe Sheng
In this paper, a symplectic structure on a Leibniz algebra is defined to be a nondegenerate bilinear form satisfying certain compatibility condition, and a phase space of a Leibniz algebra is defined to be a symplectic Leibniz algebra satisfying certain conditions. We show that a Leibniz algebra has a phase space if and only if there is a compatible Leibniz-dendriform algebra, and phase spaces of Leibniz
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Certain functional identities on division rings J. Algebra (IF 0.9) Pub Date : 2024-03-08 Tsiu-Kwen Lee, Jheng-Huei Lin
We study the functional identity on a division ring , where is an additive map and are generalized polynomials in the variable with coefficients in . Precisely, it is proved that either is finite-dimensional over its center or is an elementary operator. Applying the result and its consequences, we prove that if is a noncommutative division ring of characteristic not 2, then the only solution of additive
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Generalized versality, special points, and resolvent degree for the sporadic groups J. Algebra (IF 0.9) Pub Date : 2024-03-05 Claudio Gómez-Gonzáles, Alexander J. Sutherland, Jesse Wolfson
Resolvent degree is an invariant measuring the complexity of algebraic and geometric phenomena, including the complexity of finite groups. To date, the resolvent degree of a finite simple group has only been investigated when is a cyclic group; an alternating group; a simple factor of a Weyl group of type , , or ; or . In this paper, we establish upper bounds on the resolvent degrees of the sporadic
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An algebraic framework for the Drinfeld double based on infinite groupoids J. Algebra (IF 0.9) Pub Date : 2024-03-05 Nan Zhou, Shuanhong Wang
In this paper we mainly consider the notion of Drinfeld double for two weak multiplier Hopf (⁎-)algebras which are paired with each other. Then we show that the Drinfeld double is again a weak multiplier Hopf (⁎-)algebra. Furthermore, we study integrals on the Drinfeld double. Finally, we establish the correspondence between modules over a Drinfeld double and Yetter-Drinfeld modules over a weak algebraic
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Transposed Poisson structures on Lie incidence algebras J. Algebra (IF 0.9) Pub Date : 2024-03-05 Ivan Kaygorodov, Mykola Khrypchenko
Let be a finite connected poset, a field of characteristic zero and the incidence algebra of over seen as a Lie algebra under the commutator product. In the first part of the paper we show that any -derivation of decomposes into the sum of a central-valued -derivation, an inner -derivation and a -derivation associated with a map that is constant on chains and cycles in . In the second part of the paper
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Sequence-regular commutative DG-rings J. Algebra (IF 0.9) Pub Date : 2024-03-05 Liran Shaul
We introduce a new class of commutative noetherian DG-rings which generalizes the class of regular local rings. These are defined to be local DG-rings such that the maximal ideal can be generated by an -regular sequence. We call these DG-rings sequence-regular DG-rings, and make a detailed study of them. Using methods of Cohen-Macaulay differential graded algebra, we prove that the Auslander-Buchsbaum-Serre
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A connectedness theorem for spaces of valuation rings J. Algebra (IF 0.9) Pub Date : 2024-03-04 William Heinzer, K. Alan Loper, Bruce Olberding, Matthew Toeniskoetter
Let be a field, let be a local subring of , and let be the space of valuation rings of that dominate . We lift Zariski's connectedness theorem for fibers of a projective morphism to the Zariski-Riemann space of valuation rings of by proving that a subring of dominating is local, residually algebraic over and integrally closed in if and only if there is a closed and connected subspace of such that is
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Homological representations of low genus mapping class groups J. Algebra (IF 0.9) Pub Date : 2024-03-04 Trent Lucas
Given a finite group acting on a surface , the centralizer of in the mapping class group has a natural representation given by its action on the homology . We consider the question of whether this representation has arithmetic image. Several authors have given positive and negative answers to this question. We give a complete answer when has genus at most 3.
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Reflective obstructions of unitary modular varieties J. Algebra (IF 0.9) Pub Date : 2024-03-04 Yota Maeda
To prove that a modular variety is of general type, there are three types of obstructions: reflective, cusp and elliptic obstructions. In this paper, we give a quantitative estimate of the reflective obstructions for the unitary case. This shows in particular that the reflective obstructions are small enough in higher dimension, say greater than 138. Our result reduces the study of the Kodaira dimension
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Spectral equivalence of smooth group schemes over principal ideal local rings J. Algebra (IF 0.9) Pub Date : 2024-03-04 Itamar Hadas
Let be a smooth linear group scheme of finite type. For any positive integer and a finite field , let be the ring of Witt vectors of length over . We show that the group algebras of and are isomorphic (i.e. the multi-sets of the dimensions of the irreducible representations are equal) for any positive integer and finite field with large enough characteristic. We also prove that if is large enough,
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On p-groups with a maximal elementary abelian normal subgroup of rank k J. Algebra (IF 0.9) Pub Date : 2024-03-01 Zoltán Halasi, Károly Podoski, László Pyber, Endre Szabó
There are several results in the literature concerning -groups with a maximal elementary abelian normal subgroup of rank due to Thompson, Mann and others. Following an idea of Sambale we obtain bounds for the number of generators etc. of a 2-group in terms of , which were previously known only for . We also prove a theorem that is new even for odd primes. Namely, we show that if has a maximal elementary
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Valuative dimension, constructive points of view J. Algebra (IF 0.9) Pub Date : 2024-03-01 Henri Lombardi, Stefan Neuwirth, Ihsen Yengui
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content
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Derivations, extensions, and rigidity of subalgebras of the Witt algebra J. Algebra (IF 0.9) Pub Date : 2024-03-01 Lucas Buzaglo
Let be an algebraically closed field of characteristic 0. We study some cohomological properties of Lie subalgebras of the Witt algebra and the one-sided Witt algebra . In the first part of the paper, we consider finite codimension subalgebras of . We compute derivations and one-dimensional extensions of such subalgebras. These correspond to , where is a subalgebra of and is a one-dimensional representation
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The Hilbert function of general unions of lines and double lines in the projective space J. Algebra (IF 0.9) Pub Date : 2024-03-01 Edoardo Ballico
We study the Hilbert function of a general union of double lines and lines. In many cases (e.g. always for and or for and or for and ) we prove that has maximal rank. We give a few examples of and for which has not maximal rank.
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Universal co-extensions of torsion abelian groups J. Algebra (IF 0.9) Pub Date : 2024-03-01 Alejandro Argudín-Monroy, Carlos E. Parra
In , a theory of universal extensions in abelian categories is developed; in particular, the notion of -universal object is presented. In the present paper, we show that an Ab3 abelian category which is -small satisfies the Ab4 condition if, and only if, each one of its objects is -universal. We use the dual of this result to construct projective effacements in Grothendieck categories. In particular
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Criteria for supersolvability of saturated fusion systems J. Algebra (IF 0.9) Pub Date : 2024-03-01 Fawaz Aseeri, Julian Kaspczyk
Let be a prime number. A saturated fusion system on a finite -group is said to be if there is a series of subgroups of such that is strongly -closed for all and such that is cyclic for all . We prove some criteria that ensure that a saturated fusion system on a finite -group is supersolvable provided that certain subgroups of are abelian and weakly -closed. Our results can be regarded as generalizations
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The R-matrix presentation for the rational form of a quantized enveloping algebra J. Algebra (IF 0.9) Pub Date : 2024-03-01 Matthew Rupert, Curtis Wendlandt
Let denote the rational form of the quantized enveloping algebra associated to a complex simple Lie algebra . Let be a nonzero dominant integral weight of , and let be the corresponding type 1 finite-dimensional irreducible representation of . Starting from this data, the -matrix formalism for quantum groups outputs a Hopf algebra defined in terms of a pair of generating matrices satisfying well-known
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The field of moduli of a divisor on a rational curve J. Algebra (IF 0.9) Pub Date : 2024-03-01 Giulio Bresciani
Let be a field with algebraic closure and a reduced, effective divisor of degree , write for the field of moduli of . A. Marinatto proved that when is odd, or , descends to a divisor on .
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Solubilizers in profinite groups J. Algebra (IF 0.9) Pub Date : 2024-03-01 Andrea Lucchini
The solubilizer of an element of a profinite group is the set of the elements of such that the subgroup of generated by and is prosoluble. We propose the following conjecture: the solubilizer of in has positive Haar measure if and only if centralizes ‘almost all’ the non-abelian chief factors of . We reduce the proof of this conjecture to another conjecture concerning finite almost simple groups: there
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Orbifold theory for vertex algebras and Galois correspondence J. Algebra (IF 0.9) Pub Date : 2024-02-29 Chongying Dong, Li Ren, Chao Yang
Let be a simple vertex algebra of countable dimension, be a finite automorphism group of and be a central element of . Assume that is a finite set of inequivalent irreducible -twisted -modules such that is invariant under the action of . Then there is a finite dimensional semisimple associative algebra for a suitable 2-cocycle naturally determined by the -action on such that form a dual pair on the
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Tensor 2-Product for sl2: Extensions to the Negative Half J. Algebra (IF 0.9) Pub Date : 2024-02-29 Matthew McMillan
In a recent paper, the author defined an operation of tensor product for a large class of 2-representations of , the positive half of the 2-category associated to . In this paper, we prove that the operation extends to give an operation of tensor product for 2-representations of the full 2-category : when the inputs are 2-representations of the full , the 2-product is also a 2-representation of the
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On positivity of Roger–Yang skein algebras J. Algebra (IF 0.9) Pub Date : 2024-02-29 Hiroaki Karuo
We generalize the positivity conjecture on (Kauffman bracket) skein algebras to Roger–Yang skein algebras. To generalize it, we use Chebyshev polynomials of the first kind to give candidates of positive bases. Moreover, the polynomials form a lower bound in the sense of and . We also discuss a relation between the polynomials and the centers of Roger–Yang skein algebras when the quantum parameter is
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Efficient generation of ideals and an analogue of a result of Mohan Kumar J. Algebra (IF 0.9) Pub Date : 2024-02-29 Jebasingh R, Md. Ali Zinna
Let be a field and be a discrete Hodge algebra of dimension over . Let be an ideal such that and , where stands for the minimal number of generators. Then we prove that . In other words, is efficiently generated. We also show that the bound can be improved if the base field . As applications, we prove some interesting results on set-theoretic generation of ideals in a discrete Hodge algebra.
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Unbounded twisted complexes J. Algebra (IF 0.9) Pub Date : 2024-02-29 Rina Anno, Timothy Logvinenko
We define unbounded twisted complexes and bicomplexes generalising the notion of a (bounded) twisted complex over a DG category . These need to be considered relative to another DG category admitting countable direct sums and shifts. The resulting DG category of unbounded twisted complexes has a fully faithful convolution functor into which factors through if the latter is closed under twisting. As
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Toward cohomology rings of intersections of Peterson varieties and Richardson varieties J. Algebra (IF 0.9) Pub Date : 2024-02-29 Tatsuya Horiguchi
Peterson varieties are subvarieties of flag varieties and their (equivariant) cohomology rings are given by Fukukawa–Harada–Masuda in type and soon later the author with Harada and Masuda gives an explicit presentation of the (equivariant) cohomology rings of Peterson varieties for arbitrary Lie types. In this note we study the (equivariant) cohomology ring of the intersections of Peterson variety
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Igusa-Todorov and LIT algebras on Morita context algebras J. Algebra (IF 0.9) Pub Date : 2024-02-29 Marcos Barrios, Gustavo Mata
In this article, we prove that, under certain conditions, Morita context algebras that arise from Igusa-Todorov (LIT) algebras and have zero bimodule morphisms are also Igusa-Todorov (LIT). For a finite dimensional algebra , we prove that the class is a 0-Igusa-Todorov subcategory if and only if is selfinjective or . As a consequence is an algebra if and only if is selfinjective or . We also show that
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On the graph products of simplicial groups and connected Hopf algebras J. Algebra (IF 0.9) Pub Date : 2024-02-28 Li Cai
In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these graph products are models of the loop spaces of polyhedral products over a flag complex and their homology, respectively. Certain morphisms between graph products
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Freiheitssatz for amalgamated products of free groups over maximal cyclic subgroups J. Algebra (IF 0.9) Pub Date : 2024-02-28 Carsten Feldkamp
In 1930, Wilhelm Magnus introduced the so-called Freiheitssatz: Let be a free group with basis and let be a cyclically reduced element of which contains a basis element , then every non-trivial element of the normal closure of in contains the basis element . Equivalently, the subgroup freely generated by embeds canonically into the quotient group . In this article, we want to introduce a Freiheitssatz
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Symplectic orbits of unimodular rows J. Algebra (IF 0.9) Pub Date : 2024-02-28 Tariq Syed
For a smooth affine algebra of dimension over a field and an invertible alternating matrix of rank 2, the group of invertible matrices of rank 2 over which are symplectic with respect to acts on the right on the set of unimodular rows of length 2 over . In this paper, we prove that acts transitively on if is algebraically closed, and .
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Plenary train algebras of rank m and backcrossing identity J. Algebra (IF 0.9) Pub Date : 2024-02-28 Joseph Bayara, Siaka Coulibaly
This paper concerns commutative plenary train algebras of rank and their idempotents. We obtain the Peirce decomposition of these algebras having an idempotent element and the multiplication table of Peirce components when the plenary train roots are mutually different. We show that a backcrossing algebra is a plenary train algebra of rank if and only if, it is a principal train one of rank . For the
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A generalization of Alperin Fusion theorem and its applications J. Algebra (IF 0.9) Pub Date : 2024-02-28 M. Yası̇r Kızmaz
Let be a saturated fusion system on a finite -group , and let be a strongly -closed subgroup of . We define the concept “-essential subgroups with respect to ” which are some proper subgroups of satisfying some technical conditions and show that an -isomorphism between subgroups of can be factorized by some automorphisms of and -essential subgroups with respect to . When is taken to be equal to , the
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Monic inversion principle and complete intersection J. Algebra (IF 0.9) Pub Date : 2024-02-23 Manoj K. Keshari, Soumi Tikader
Let be a regular ring of dimension essentially of finite type over an infinite field of characteristic ≠2. Let be a projective -module of rank with . Let be an ideal of of height and be a surjection. If has a surjective lift , then has a surjective lift . The case is due to Das-Tikader-Zinna .
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Ext modules related to syzygies of the residue field J. Algebra (IF 0.9) Pub Date : 2024-02-21 Yuya Otake
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Intersection of duality and derivation relations for multiple zeta values J. Algebra (IF 0.9) Pub Date : 2024-02-20 Aiki Kimura
The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but it remains unclear as to whether all duality relations can be deduced from the EDSR. In the present paper, regarding the family generated by the duality relation
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On the automorphisms of the Drinfel'd double of a Borel Lie subalgebra J. Algebra (IF 0.9) Pub Date : 2024-02-20 Michaël Bulois, Nicolas Ressayre
Let be a complex simple Lie algebra with a Borel subalgebra . Consider the semidirect product , where the dual of is equipped with the coadjoint action of and is considered as an abelian ideal of . We describe the automorphism group of the Lie algebra . In particular we prove that it contains the automorphism group of the extended Dynkin diagram of . In type , the dihedral subgroup was recently proved
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Height reduction for local uniformization of varieties and non-archimedean spaces J. Algebra (IF 0.9) Pub Date : 2024-02-20 Michael Temkin
It is known since the works of Zariski that the essential difficulty in the local uniformization problem is met already in the case of valuations of height one. In this paper we prove that local uniformization of schemes and non-archimedean analytic spaces rigorously follows from the case of valuations of height one. For non-archimedean spaces this result reduces the problem to studying local structure
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Hearts of twin cotorsion pairs revisited: Integral and Abelian hearts J. Algebra (IF 0.9) Pub Date : 2024-02-20 Yu Liu, Panyue Zhou
Hearts of twin cotorsion pairs are shown to be quasi-abelian in . But they are not always integral. In this article, we provide a sufficient and necessary condition for the hearts of twin cotorsion pairs being integral (resp. abelian).
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Conformal vector fields on Lie groups: The trans-Lorentzian signature J. Algebra (IF 0.9) Pub Date : 2024-02-19 Hui Zhang, Zhiqi Chen, Ju Tan
A pseudo-Riemannian Lie group is a connected Lie group endowed with a left-invariant pseudo-Riemannian metric of signature . In this paper, we study pseudo-Riemannian Lie groups with non-Killing left-invariant conformal vector fields. Firstly, we prove that if is a Cartan subalgebra for a semisimple Levi factor of the Lie algebra , then . Secondly, we classify trans-Lorentzian Lie groups (i.e., ) with
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Finitely generated saturated multi-Rees algebras J. Algebra (IF 0.9) Pub Date : 2024-02-19 Suprajo Das, Sudeshna Roy
We study the question of finite generation of saturated multi-Rees algebras and investigate the asymptotic behaviour of related length functions. In the setup of excellent local domains, we show that the saturated multi-Rees algebra of a finite collection of ideals is finitely generated when the analytic spread is not maximal and the associated length function eventually agrees with a polynomial. Similar
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Perazzo hypersurfaces and the weak Lefschetz property J. Algebra (IF 0.9) Pub Date : 2024-02-19 Rosa M. Miró-Roig, Josep Pérez
We deal with Perazzo hypersurfaces in defined by a homogeneous polynomial , where are algebraically dependent but linearly independent forms of degree in and is a form in of degree . Perazzo hypersurfaces have vanishing hessian and, hence, the associated graded artinian Gorenstein algebra fails the strong Lefschetz property. In this paper, we first determine the maximum and minimum Hilbert function
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On the component group of the algebraic monodromy group of a K3 surface J. Algebra (IF 0.9) Pub Date : 2024-02-15 Andreas-Stephan Elsenhans, Jörg Jahnel
We provide a lower bound for the number of components of the algebraic monodromy group in the situation of a 3 surface over a number field . In the CM case, our bound is sharp. As an application, we describe, in the case of CM, the jump character entirely in terms of the endomorphism field and the geometric Picard rank.
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Large norms in group theory J. Algebra (IF 0.9) Pub Date : 2024-02-15 Maria Ferrara, Marco Trombetti
In 1935, the introduction of the of a group by Reinhold Baer is a turning point in group theory. In fact, Baer proved that there is a very strong relationship between the structure of the norm and that of the whole group (see , , , , ). Since then, the norm has been playing a very significant roles in many aspects of group theory and its applications: it has been used in to describe the connection
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Local, colocal, and antilocal properties of modules and complexes over commutative rings J. Algebra (IF 0.9) Pub Date : 2024-02-15 Leonid Positselski
This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are locally controlled in a finite affine open covering. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while
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A finite-dimensional singular superalgebra is algebraically generated J. Algebra (IF 0.9) Pub Date : 2024-02-13 Sergey Pchelintsev, Oleg Shashkov
This article is the final one in the series of papers by the authors devoted to finite-dimensional singular (simple right-alternative with zero product in the even part) superalgebras. In previous papers, algebraically generated singular superalgebras were studied and it was proved that any such superalgebra has the structure of an extended double. In this article, we prove that any singular superalgebra
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Separable MV-algebras and lattice-ordered groups J. Algebra (IF 0.9) Pub Date : 2024-02-13 Vincenzo Marra, Matías Menni
The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra . Beyond its intrinsic algebraic interest, this research
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Geometry of smooth extremal surfaces J. Algebra (IF 0.9) Pub Date : 2024-02-13 Anna Brosowsky, Janet Page, Tim Ryan, Karen E. Smith
We study the geometry of smooth projective surfaces defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces , and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces. For instance, extremal
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Dimension results for extremal-generic polynomial systems over complete toric varieties J. Algebra (IF 0.9) Pub Date : 2024-02-13 Matías Bender, Pierre-Jean Spaenlehauer
We study polynomial systems with prescribed monomial supports in the Cox ring of a toric variety built from a complete polyhedral fan. We present combinatorial formulas for the dimension of their associated subvarieties under genericity assumptions on the coefficients of the polynomials. Using these formulas, we identify at which degrees generic systems in polytopal algebras form regular sequences
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Extension dimensions of derived and stable equivalent algebras J. Algebra (IF 0.9) Pub Date : 2024-02-13 Jinbi Zhang, Junling Zheng
The extension dimensions of an Artin algebra give a reasonable way of measuring how far an algebra is from being representation-finite. In this paper we mainly study the behavior of the extensions dimensions of algebras under different equivalences. We show that the difference of the extension dimensions of two derived equivalent algebras is bounded above by the length of the tilting complex associated
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The completion of d-abelian categories J. Algebra (IF 0.9) Pub Date : 2024-02-12 Ramin Ebrahimi, Alireza Nasr-Isfahani
Let be a finite-dimensional algebra, and be a -cluster tilting subcategory of mod . From the viewpoint of higher homological algebra, a natural question to ask is when induces a -cluster tilting subcategory in Mod . In this paper, we investigate this question in a more general form. We consider as an essentially small -abelian category, known to be equivalent to a -cluster tilting subcategory of an
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On homological properties of the category of [formula omitted]-representations over a linear quiver of type [formula omitted] J. Algebra (IF 0.9) Pub Date : 2024-02-12 Changjian Fu, Longjun Ran, Liang Yang
Let be a quiver of type with linear orientation and the category of representations of over the virtual field . It is proved that has global dimension 2 whenever and it is hereditary if . As a consequence, the Euler form is well-defined. However, it does not descend to the Grothendieck group of . This yields negative answers to questions raised by Szczesny (2012) .
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Cohomologies of difference Lie groups and the van Est theorem J. Algebra (IF 0.9) Pub Date : 2024-02-12 Jun Jiang, Yunnan Li, Yunhe Sheng
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group, and establish the relation between representations of difference Lie groups and representations of difference Lie algebras via differentiation and integration. Then
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The pro-supersolvable topology on a free group: Deciding denseness J. Algebra (IF 0.9) Pub Date : 2024-02-10 Claude Marion, Pedro V. Silva, Gareth Tracey
Let be a free group of arbitrary rank and let be a finitely generated subgroup of . Given a pseudovariety of finite groups, i.e. a class of finite groups closed under taking subgroups, quotients and finitary direct products, we endow with its pro- topology. Our main result states that it is decidable whether is pro- dense, where denote respectively the pseudovarieties of all finite supersolvable groups
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Gluing simple-minded collections in triangulated categories J. Algebra (IF 0.9) Pub Date : 2024-02-10 Yongliang Sun, Yaohua Zhang
We provide a technique to glue simple-minded collections along a recollement of Hom-finite Krull-Schmidt triangulated categories over a field. This gluing technique for simple-minded collections is shown to be compatible with those for gluing bounded -structures, silting objects, and co--structures in the literature. Furthermore, it also enjoys the properties of preserving partial order and commuting
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The Lie coalgebra of multiple polylogarithms J. Algebra (IF 0.9) Pub Date : 2024-02-10 Zachary Greenberg, Dani Kaufman, Haoran Li, Christian K. Zickert
We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, which we think of as functional relations for multiple polylogarithms. In particular, we have inversion relations and shuffle relations. We relate our definition to Goncharov's Bloch groups, and to the concrete model for by Goncharov
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k-torsionfree modules and Frobenius extensions J. Algebra (IF 0.9) Pub Date : 2024-02-10 Zhibing Zhao
Let be a Frobenius extension and be a positive integer. We prove that an -module is -torsionfree if and only if so is its underlying -module. As an application, we obtain that if is a quasi -Gorenstein ring then so is , but the converse does not hold in general.
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On the orders of composition factors in completely reducible groups J. Algebra (IF 0.9) Pub Date : 2024-02-08 Attila Maróti, Saveliy V. Skresanov
We obtain an asymptotic upper bound for the product of the -parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime . This enables us to give a new bound for the diameter of a nondiagonal orbital graph of an affine primitive permutation group.
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An SL(3,C)-equivariant smooth compactification of moduli space of rational quartic plane curves J. Algebra (IF 0.9) Pub Date : 2024-02-07 Kiryong Chung, Jeong-Seop Kim
Let be the space of stable sheaves which satisfy the Hilbert polynomial and are supported on rational curves in the projective plane . Then (resp. ) is isomorphic to (resp. ). In addition, is well-known to be a -bundle over . In particular, is smooth for . However, for , in general, the space is no longer smooth because of the complexity of boundary curves. In this paper, we obtained an -equivariant