Journal of Algebra最新文献

Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-20 DOI: 10.1016/j.jalgebra.2025.03.013

Xu Gao , Jianqi Liu , Yiyi Zhu

引用次数: 0

Convex hulls of curves in n-space

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-20 DOI: 10.1016/j.jalgebra.2025.03.018

Claus Scheiderer

{"title":"Convex hulls of curves in n-space","authors":"Claus Scheiderer","doi":"10.1016/j.jalgebra.2025.03.018","DOIUrl":"10.1016/j.jalgebra.2025.03.018","url":null,"abstract":"<div><div>Let <math><mi>K</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> be a convex semialgebraic set. The semidefinite extension degree <math><mi>sxdeg</mi><mo>(</mo><mi>K</mi><mo>)</mo></math> of K is the smallest number d such that K is a linear image of an intersection of finitely many spectrahedra, each of which is described by a linear matrix inequality of size ≤d. This invariant can be considered to be a measure for the intrinsic complexity of semidefinite optimization over the set K. For an arbitrary semialgebraic set <math><mi>S</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> of dimension one, our main result states that the closed convex hull K of S satisfies <math><mi>sxdeg</mi><mo>(</mo><mi>K</mi><mo>)</mo><mo>≤</mo><mn>1</mn><mo>+</mo><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></math>. This bound is best possible in several ways. Before, the result was known for <math><mi>n</mi><mo>=</mo><mn>2</mn></math>, and also for general n in the case when S is a monomial curve.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 314-340"},"PeriodicalIF":0.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Corrigendum to “Representation stability for diagram algebras” [J. Algebra 638 (2024) 625–669]

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-18 DOI: 10.1016/j.jalgebra.2025.03.004

Peter Patzt

引用次数: 0

Gradings, graded identities, ⁎-identities and graded ⁎-identities of an algebra of upper triangular matrices

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jalgebra.2025.02.047

Jonatan Andres Gomez Parada, Plamen Koshlukov

引用次数: 0

Membership problems in finite groups

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jalgebra.2025.03.011

Markus Lohrey , Andreas Rosowski , Georg Zetzsche

{"title":"Membership problems in finite groups","authors":"Markus Lohrey , Andreas Rosowski , Georg Zetzsche","doi":"10.1016/j.jalgebra.2025.03.011","DOIUrl":"10.1016/j.jalgebra.2025.03.011","url":null,"abstract":"<div><div>We show that the subset sum problem, the knapsack problem and the rational subset membership problem for permutation groups are NP-complete. Concerning the knapsack problem we obtain NP-completeness for every fixed <math><mi>n</mi><mo>≥</mo><mn>3</mn></math>, where n is the number of permutations in the knapsack equation. In other words: membership in products of three cyclic permutation groups is NP-complete. This sharpens a result of Luks [34], which states NP-completeness of the membership problem for products of three abelian permutation groups. We also consider the context-free membership problem in permutation groups and prove that it is PSPACE-complete but NP-complete for a restricted class of context-free grammars where acyclic derivation trees must have constant Horton-Strahler number. Our upper bounds hold for black box groups. The results for context-free membership problems in permutation groups yield new complexity bounds for various intersection non-emptiness problems for DFAs and a single context-free grammar. This paper is an extended version of the conference paper [31].</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"675 ","pages":"Pages 23-58"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Representations and cohomologies of the alternating group of degree 4 4 度交替群的表示和同调

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jalgebra.2025.02.042

Yuriy Drozd , Andriana Plakosh

引用次数: 0

Broué's conjecture for isolated RoCK blocks of finite odd-dimensional orthogonal groups 有限奇维正交群的孤立 RoCK 块的布劳埃猜想

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jalgebra.2025.02.045

Pengcheng Li , Yanjun Liu , Jiping Zhang

引用次数: 0

G-tables and the Poisson structure of the even cohomology of cotangent bundle of the Heisenberg Lie group

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jalgebra.2025.02.040

Leandro Cagliero , Gonzalo Gutierrez

引用次数: 0

Radicals in polynomial rings skewed by an endomorphism

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-14 DOI: 10.1016/j.jalgebra.2025.02.044

Nam Kyun Kim , Pace P. Nielsen , Michał Ziembowski

{"title":"Radicals in polynomial rings skewed by an endomorphism","authors":"Nam Kyun Kim , Pace P. Nielsen , Michał Ziembowski","doi":"10.1016/j.jalgebra.2025.02.044","DOIUrl":"10.1016/j.jalgebra.2025.02.044","url":null,"abstract":"<div><div>Given a ring R, radicals of the polynomial ring <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>]</mo></math>, and even of the skew polynomial ring <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>;</mo><mi>σ</mi><mo>]</mo></math> skewed by an endomorphism σ on R, have been studied and described for many different radicals. Often, in those descriptions, the ring R was assumed to be unital, or the endomorphism σ was assumed to be an automorphism. Here we systematically study what happens when such assumptions are dropped, and generalize to even more radicals. Our results reveal three key properties that, when present, allow a simple description of a radical of <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>;</mo><mi>σ</mi><mo>]</mo></math>. Moreover, multiple examples are provided showing that when σ is injective, but not surjective, wild growth patterns may occur.</div><div>We also answer an open question in the literature, by showing that the Levitzki radical of the skew Laurent polynomial ring <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>,</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>;</mo><mi>σ</mi><mo>]</mo></math> (when σ is an automorphism) is not naively describable in terms of the Levitzki radicals of <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>;</mo><mi>σ</mi><mo>]</mo></math> and <math><mi>R</mi><mo>[</mo><mi>x</mi><mo>;</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>]</mo></math>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 117-142"},"PeriodicalIF":0.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Affine flag varieties of type D

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-03-14 DOI: 10.1016/j.jalgebra.2025.02.043

Quanyong Chen, Zhaobing Fan, Qi Wang

引用次数: 0