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An extension of the group of flows method for finite pre-Lie rings 有限预李环流动群方法的推广
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-10 DOI: 10.1016/j.jpaa.2025.108128
Agata Smoktunowicz
{"title":"An extension of the group of flows method for finite pre-Lie rings","authors":"Agata Smoktunowicz","doi":"10.1016/j.jpaa.2025.108128","DOIUrl":"10.1016/j.jpaa.2025.108128","url":null,"abstract":"<div><div>This paper presents an extension of the classical method <span><span>[1]</span></span> for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <em>p</em> prime and <em>n</em> larger than <em>p</em> can be obtained with our extension.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108128"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528932","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
A Tate algebra version of the Jacobian conjecture 雅可比猜想的泰特代数版本
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-10 DOI: 10.1016/j.jpaa.2025.108129
Lucas Hamada, Kazuki Kato, Ryo Komiya
{"title":"A Tate algebra version of the Jacobian conjecture","authors":"Lucas Hamada,&nbsp;Kazuki Kato,&nbsp;Ryo Komiya","doi":"10.1016/j.jpaa.2025.108129","DOIUrl":"10.1016/j.jpaa.2025.108129","url":null,"abstract":"<div><div>This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as <em>the Tate-Jacobian conjecture</em>, for commutative rings <em>R</em> equipped with an <em>I</em>-adic topology. We show that if the <em>I</em>-adic topology on <em>R</em> is Hausdorff and <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> is a subring of a <span><math><mi>Q</mi></math></span>-algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for <span><math><mi>C</mi></math></span> is equivalent to the following statement: for all but finitely many primes <em>p</em>, the inverse of a polynomial map over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> whose Jacobian determinant is an element of <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>×</mo></mrow></msubsup></math></span> lies in the Tate algebra over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108129"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528933","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
Starfish lemma via birational quasi-isomorphisms 通过两族拟同构的海星引理
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-07 DOI: 10.1016/j.jpaa.2025.108127
Dmitriy Voloshyn
{"title":"Starfish lemma via birational quasi-isomorphisms","authors":"Dmitriy Voloshyn","doi":"10.1016/j.jpaa.2025.108127","DOIUrl":"10.1016/j.jpaa.2025.108127","url":null,"abstract":"<div><div>We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108127"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528934","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
Idempotent completion of persistence categories 持久性范畴的幂等补全
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-19 DOI: 10.1016/j.jpaa.2025.108136
John G. Miller
{"title":"Idempotent completion of persistence categories","authors":"John G. Miller","doi":"10.1016/j.jpaa.2025.108136","DOIUrl":"10.1016/j.jpaa.2025.108136","url":null,"abstract":"<div><div>This paper studies how persistence categories and triangulated persistence categories behave with respect to taking idempotent completions. In particular we study when the idempotent completion (Karoubi envelope) of categories admitting persistence refinement also admits such a refinement. In doing so, we introduce notions of persistence semi-categories and persistent presheaves and explore their properties.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108136"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623946","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
On tensor products of representations of Lie superalgebras 李超代数表示的张量积
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-10 DOI: 10.1016/j.jpaa.2025.108130
Abhishek Das , Santosha Pattanayak
{"title":"On tensor products of representations of Lie superalgebras","authors":"Abhishek Das ,&nbsp;Santosha Pattanayak","doi":"10.1016/j.jpaa.2025.108130","DOIUrl":"10.1016/j.jpaa.2025.108130","url":null,"abstract":"<div><div>We consider typical finite dimensional complex irreducible representations of a basic classical Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for <span><math><mrow><mi>sl</mi></mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mrow><mi>osp</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>)</mo></math></span>, <span><math><mi>G</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> and <span><math><mi>F</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span> under some assumptions. This result is a Lie superalgebra analogue of Rajan's fundamental result <span><span>[10]</span></span> on unique factorization of tensor products for finite dimensional complex simple Lie algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108130"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579725","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
Quotients of the braid group that are extensions of the symmetric group 编织群的商是对称群的扩展
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-12-02 DOI: 10.1016/j.jpaa.2025.108138
Matthew B. Day , Trevor Nakamura
{"title":"Quotients of the braid group that are extensions of the symmetric group","authors":"Matthew B. Day ,&nbsp;Trevor Nakamura","doi":"10.1016/j.jpaa.2025.108138","DOIUrl":"10.1016/j.jpaa.2025.108138","url":null,"abstract":"<div><div>We consider normal subgroups <em>N</em> of the braid group <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> such that the quotient <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><mi>N</mi></math></span> is an extension of the symmetric group by an abelian group. We show that, if <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, then there are exactly 8 commensurability classes of such subgroups. We define a <em>Specht subgroup</em> to be a subgroup of this form that is maximal in its commensurability class. We give descriptions of the Specht subgroups in terms of winding numbers and in terms of infinite generating sets. The quotient of the pure braid group by a Specht subgroup is a module over the symmetric group. We show that the modules arising this way are closely related to Specht modules for the partitions <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, working over the integers. We compute the second cohomology of the symmetric group with coefficients in both of these Specht modules, working over an arbitrary commutative ring. Finally, we determine which of the extensions of the symmetric group arising from Specht subgroups are split extensions.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108138"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747650","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
Restrictions on Hilbert coefficients give depths of graded domains 希尔伯特系数的限制给出了梯度域的深度
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-12-02 DOI: 10.1016/j.jpaa.2025.108144
Cheng Meng
{"title":"Restrictions on Hilbert coefficients give depths of graded domains","authors":"Cheng Meng","doi":"10.1016/j.jpaa.2025.108144","DOIUrl":"10.1016/j.jpaa.2025.108144","url":null,"abstract":"<div><div>In this paper, we prove that if <em>P</em> is a homogeneous prime ideal inside a standard graded polynomial ring <em>S</em> with <span><math><mi>dim</mi><mo>⁡</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>P</mi><mo>)</mo><mo>=</mo><mi>d</mi></math></span>, and for <span><math><mi>s</mi><mo>≤</mo><mi>d</mi></math></span>, adjoining <em>s</em> general linear forms to the prime ideal changes the <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mi>s</mi><mo>)</mo></math></span>-th Hilbert coefficient by 1, then <span><math><mtext>depth</mtext><mo>(</mo><mi>S</mi><mo>/</mo><mi>P</mi><mo>)</mo><mo>=</mo><mi>s</mi><mo>−</mo><mn>1</mn></math></span>. This criterion also tells us about possible restrictions on the generic initial ideal of a prime ideal inside a polynomial ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108144"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693706","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
Differential identities of the Grassmann algebra 格拉斯曼代数的微分恒等式
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-12-02 DOI: 10.1016/j.jpaa.2025.108143
Onofrio M. Di Vincenzo , Vincenzo C. Nardozza
{"title":"Differential identities of the Grassmann algebra","authors":"Onofrio M. Di Vincenzo ,&nbsp;Vincenzo C. Nardozza","doi":"10.1016/j.jpaa.2025.108143","DOIUrl":"10.1016/j.jpaa.2025.108143","url":null,"abstract":"<div><div>Let <em>F</em> be a field of characteristic zero and let <em>E</em> be the Grassmann algebra of an infinite-dimensional <em>F</em>-vector space. We consider a class of solvable nonabelian finite-dimensional Lie algebras acting on <em>E</em> by derivations, and completely describe the differential polynomial identities satisfied by <em>E</em>. The corresponding <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-cocharacter and differential codimension sequences are computed. Finally, we prove that the differential exponent exists and equals the ordinary exponent of <em>E</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108143"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693705","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
Preprojective algebras, skew group algebras and Morita equivalences 预投影代数、斜群代数与森田等价
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-12-02 DOI: 10.1016/j.jpaa.2025.108141
Xiao-Wu Chen , Ren Wang
{"title":"Preprojective algebras, skew group algebras and Morita equivalences","authors":"Xiao-Wu Chen ,&nbsp;Ren Wang","doi":"10.1016/j.jpaa.2025.108141","DOIUrl":"10.1016/j.jpaa.2025.108141","url":null,"abstract":"<div><div>Let <span><math><mi>K</mi></math></span> be a field of characteristic <em>p</em> and <em>G</em> be a cyclic <em>p</em>-group which acts on a finite acyclic quiver <em>Q</em>. The folding process associates a Cartan triple to the action. We establish a Morita equivalence between the skew group algebra of the preprojective algebra of <em>Q</em> and the generalized preprojective algebra associated to the Cartan triple in the sense of Geiss, Leclerc and Schröer. The Morita equivalence induces an isomorphism between certain ideal monoids of these preprojective algebras, which is compatible with the embedding of Weyl groups appearing in the folding process.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108141"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693703","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
Artin-Schelter Gorenstein property of Hopf Galois extensions Hopf - Galois扩展的Artin-Schelter Gorenstein性质
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-12-01 Epub Date: 2025-11-03 DOI: 10.1016/j.jpaa.2025.108123
Ruipeng Zhu
{"title":"Artin-Schelter Gorenstein property of Hopf Galois extensions","authors":"Ruipeng Zhu","doi":"10.1016/j.jpaa.2025.108123","DOIUrl":"10.1016/j.jpaa.2025.108123","url":null,"abstract":"<div><div>This paper investigates the homological properties of the faithfully flat Hopf Galois extension <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span>. It establishes that when <em>B</em> is a noetherian affine PI algebra and <em>A</em> is AS Gorenstein, <em>B</em> inherits the AS Gorenstein property. Furthermore, we demonstrate that injective dimension serves as a monoidal invariant for AS Gorenstein Hopf algebras. Specifically, if two such Hopf algebras have equivalent monoidal categories of comodules, then their injective dimensions are equal.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108123"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475353","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
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