Journal of Algebra最新文献

{"title":"Finite W-algebra invariants via Lax type operators","authors":"Jonathan Brown","doi":"10.1016/j.jalgebra.2025.03.019","DOIUrl":"10.1016/j.jalgebra.2025.03.019","url":null,"abstract":"<div><div>We use variations on Lax type operators to find explicit formulas for certain elements of finite <em>W</em>-algebras. These give a complete set of generators for all finite <em>W</em>-algebras of types B, C, D for which the Dynkin grading is even.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 1-26"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747361","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}

{"title":"Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules","authors":"Xu Gao ,&nbsp;Jianqi Liu ,&nbsp;Yiyi Zhu","doi":"10.1016/j.jalgebra.2025.03.013","DOIUrl":"10.1016/j.jalgebra.2025.03.013","url":null,"abstract":"<div><div>In this paper, we introduce a notion of <em>g</em>-twisted restricted conformal block on the three-pointed twisted projective line <figure><img></figure> associated with an untwisted module <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and the bottom levels of two <em>g</em>-twisted modules <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> over a vertex operator algebra <em>V</em>. We show that the space of twisted restricted conformal blocks is isomorphic to the space of <em>g</em>-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"675 ","pages":"Pages 59-132"},"PeriodicalIF":0.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737809","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}

{"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 <span><math><mi>K</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> be a convex semialgebraic set. The semidefinite extension degree <span><math><mi>sxdeg</mi><mo>(</mo><mi>K</mi><mo>)</mo></math></span> of <em>K</em> is the smallest number <em>d</em> such that <em>K</em> is a linear image of an intersection of finitely many spectrahedra, each of which is described by a linear matrix inequality of size ≤<em>d</em>. This invariant can be considered to be a measure for the intrinsic complexity of semidefinite optimization over the set <em>K</em>. For an arbitrary semialgebraic set <span><math><mi>S</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> of dimension one, our main result states that the closed convex hull <em>K</em> of <em>S</em> satisfies <span><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></span>. This bound is best possible in several ways. Before, the result was known for <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, and also for general <em>n</em> in the case when <em>S</em> 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}

{"title":"Corrigendum to “Representation stability for diagram algebras” [J. Algebra 638 (2024) 625–669]","authors":"Peter Patzt","doi":"10.1016/j.jalgebra.2025.03.004","DOIUrl":"10.1016/j.jalgebra.2025.03.004","url":null,"abstract":"","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"671 ","pages":"Pages 181-188"},"PeriodicalIF":0.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643993","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}

{"title":"Brauer characters preserve heights in p-solvable groups","authors":"Qinghong Guo ,&nbsp;Weijun Liu","doi":"10.1016/j.jalgebra.2025.03.014","DOIUrl":"10.1016/j.jalgebra.2025.03.014","url":null,"abstract":"<div><div>Let <em>p</em> be a prime number and let <em>N</em> be a normal subgroup of a finite <em>p</em>-solvable group <em>G</em>. Assume that <em>b</em> is a <em>p</em>-block of <em>N</em> with defect group <em>D</em> and <em>B</em> is a <em>p</em>-block of <em>G</em> covering <em>b</em>. Let <span><math><msup><mrow><mi>b</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> be the Brauer first main correspondent of <em>b</em> in <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, and <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> be the Harris–Knörr correspondent of <em>B</em> in <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span>. Suppose that every irreducible Brauer character in <span><math><mi>IBr</mi><mo>(</mo><mi>b</mi><mo>)</mo></math></span> is of height zero. Then there is a height preserving bijection from <span><math><mi>IBr</mi><mo>(</mo><mi>B</mi><mo>)</mo></math></span> onto <span><math><mi>IBr</mi><mo>(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span>. This is a Brauer character version of a result obtained by G. Navarro and B. Späth (2014) <span><span>[23]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 27-37"},"PeriodicalIF":0.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747362","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}

{"title":"Associative superalgebras for Z-graded vertex operator superalgebra","authors":"Huaimin Li,&nbsp;Qing Wang","doi":"10.1016/j.jalgebra.2025.03.016","DOIUrl":"10.1016/j.jalgebra.2025.03.016","url":null,"abstract":"<div><div>For a vertex superalgebra <em>V</em>, we construct a sequence of associative superalgebras <span><math><mover><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mi>V</mi><mo>)</mo></math></span> for nonnegative integer <em>n</em>, which are not depend on the conformal structure of <em>V</em>. Based on this, we show that the rationality, regularity and fusion rules are independent of the choice of the conformal vector for <span><math><mi>Z</mi></math></span>-graded vertex operator superalgebra.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 38-55"},"PeriodicalIF":0.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747363","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}

{"title":"Gradings, graded identities, ⁎-identities and graded ⁎-identities of an algebra of upper triangular matrices","authors":"Jonatan Andres Gomez Parada,&nbsp;Plamen Koshlukov","doi":"10.1016/j.jalgebra.2025.02.047","DOIUrl":"10.1016/j.jalgebra.2025.02.047","url":null,"abstract":"<div><div>Let <span><math><mi>K</mi><mo>〈</mo><mi>X</mi><mo>〉</mo></math></span> be the free associative algebra freely generated over the field <em>K</em> by the countable set <span><math><mi>X</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>}</mo></math></span>. If <em>A</em> is an associative <em>K</em>-algebra, we say that a polynomial <span><math><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>∈</mo><mi>K</mi><mo>〈</mo><mi>X</mi><mo>〉</mo></math></span> is a polynomial identity, or simply an identity in <em>A</em> if <span><math><mi>f</mi><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>0</mn></math></span> for every <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, …, <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∈</mo><mi>A</mi></math></span>.</div><div>Consider <span><math><mi>A</mi></math></span> the subalgebra of <span><math><mi>U</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>K</mi><mo>)</mo></math></span> given by:<span><span><span><math><mi>A</mi><mo>=</mo><mi>K</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>)</mo><mo>⊕</mo><mi>K</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>⊕</mo><mi>K</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>⊕</mo><mi>K</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>⊕</mo><mi>K</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> denote the matrix units. We investigate the gradings on the algebra <span><math><mi>A</mi></math></span>, determined by an abelian group, and prove that these gradings are elementary. Furthermore, we compute a basis for the <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-graded identities of <span><math><mi>A</mi></math></span>, and also for the <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-graded identities with graded involution. Moreover, we describe the cocharacters of this algebra.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 171-204"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685266","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}

{"title":"Membership problems in finite groups","authors":"Markus Lohrey ,&nbsp;Andreas Rosowski ,&nbsp;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 <strong>NP</strong>-complete. Concerning the knapsack problem we obtain <strong>NP</strong>-completeness for every fixed <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, where <em>n</em> is the number of permutations in the knapsack equation. In other words: membership in products of three cyclic permutation groups is <strong>NP</strong>-complete. This sharpens a result of Luks <span><span>[34]</span></span>, which states <strong>NP</strong>-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 <strong>PSPACE</strong>-complete but <strong>NP</strong>-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 <span><span>[31]</span></span>.</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}

{"title":"Representations and cohomologies of the alternating group of degree 4","authors":"Yuriy Drozd ,&nbsp;Andriana Plakosh","doi":"10.1016/j.jalgebra.2025.02.042","DOIUrl":"10.1016/j.jalgebra.2025.02.042","url":null,"abstract":"<div><div>We describe integral representations of the alternating group <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, in particular, the Auslander-Reiten quiver of its 2-adic representations. Using these results we calculate Tate cohomologies of all <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-lattices.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 143-154"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685264","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}

{"title":"Broué's conjecture for isolated RoCK blocks of finite odd-dimensional orthogonal groups","authors":"Pengcheng Li ,&nbsp;Yanjun Liu ,&nbsp;Jiping Zhang","doi":"10.1016/j.jalgebra.2025.02.045","DOIUrl":"10.1016/j.jalgebra.2025.02.045","url":null,"abstract":"<div><div>In a series of papers, we shall prove that Broué's abelian defect group conjecture is true for all blocks of finite odd-dimensional orthogonal groups <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span> at linear primes with <em>q</em> odd. This first paper is to prove the conjecture for isolated RoCK blocks of <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span> at odd linear primes.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"674 ","pages":"Pages 50-76"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685268","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}