Journal of Algebra最新文献_第2页

On Gelfand pairs and degenerate Gelfand-Graev modules of general linear groups of degree two over principal ideal local rings of finite length 有限长主理想局部环上一般二阶线性群的Gelfand对和退化Gelfand- graev模

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.039

Archita Gupta, Pooja Singla

{"title":"On Gelfand pairs and degenerate Gelfand-Graev modules of general linear groups of degree two over principal ideal local rings of finite length","authors":"Archita Gupta, Pooja Singla","doi":"10.1016/j.jalgebra.2025.06.039","DOIUrl":"10.1016/j.jalgebra.2025.06.039","url":null,"abstract":"<div><div>Let <em>R</em> be a principal ideal local ring of finite length with a finite residue field of odd characteristic. Denote by <span><math><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> the general linear group of degree two over <em>R</em>, and by <span><math><mi>B</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> the Borel subgroup of <span><math><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> consisting of upper triangular matrices. In this article, we prove that the pair <span><math><mo>(</mo><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>,</mo><mi>B</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>)</mo></math></span> is a strong Gelfand pair. We also investigate the decomposition of the degenerate Gelfand-Graev (DGG) modules of <span><math><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. It is known that the non-degenerate Gelfand Graev module (also called non-degenerate Whittaker model) of <span><math><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is multiplicity-free. We characterize the DGG-modules where the multiplicities are independent of the cardinality of the residue field. We provide a complete decomposition of all DGG-modules of <span><math><mi>G</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> for <em>R</em> of length at most four.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 78-108"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686803","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

Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras 群与李代数上的Rota-Baxter算子，微分算子，pre-和Novikov结构

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.044

Xing Gao , Li Guo , Zongjian Han , Yi Zhang

{"title":"Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras","authors":"Xing Gao , Li Guo , Zongjian Han , Yi Zhang","doi":"10.1016/j.jalgebra.2025.06.044","DOIUrl":"10.1016/j.jalgebra.2025.06.044","url":null,"abstract":"<div><div>Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota-Baxter operators on Lie algebras are closely related to pre-Lie algebras and post-Lie algebras. Some of their group counterparts have been introduced to study post-groups, skew left braces and set-theoretic solutions of Yang-Baxter equations, but searching suitable notions of relative Rota-Baxter operators on groups with weight zero and of pre-groups has been challenging and has been the focus of recent studies, by provisionally imposing an abelian condition.</div><div>Arising from the works of Balinsky-Novikov and Gelfand-Dorfman, Novikov algebras and their constructions from differential commutative algebras have led to broad applications. Finding their suitable counterparts for groups and Lie algebras has also attracted quite much recent interests.</div><div>This paper uses one-sided-inverse pairs of maps to give a perturbative approach to a general notion of relative Rota-Baxter operators and differential operators on a group and a Lie algebra with limit-weight. With the extra condition of limit-abelianess on the group or Lie algebra, we give an interpretation of relative Rota-Baxter and differential operators with weight zero. These operators motivate us to define pre-groups and Novikov groups respectively as the induced structures. The tangent maps of these operators on Lie groups are shown to give relative Rota-Baxter and differential operators with weight zero on Lie algebras. The tangent spaces of the pre-Lie and Novikov Lie groups are pre-Lie algebras and Novikov Lie algebras, fulfilling the expected property. Furthermore, limit-weighted relative Rota-Baxter operators on groups give rise to skew left braces and then set-theoretic solutions of the Yang-Baxter equation.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 109-148"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686804","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 the greatest semilattice decomposition of subsemigroups of regular rings 正则环子半群的最大半格分解

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.043

Xavier Mary

引用次数: 0

Shuffle product of desingularized multiple zeta functions at integer points 在整数点上的非一般化的多个zeta函数的Shuffle积

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.07.012

Nao Komiyama , Takeshi Shinohara

引用次数: 0

Counterexamples in involutions of Azumaya algebras Azumaya代数对合的反例

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.07.006

Uriya First , Ben Williams

{"title":"Counterexamples in involutions of Azumaya algebras","authors":"Uriya First , Ben Williams","doi":"10.1016/j.jalgebra.2025.07.006","DOIUrl":"10.1016/j.jalgebra.2025.07.006","url":null,"abstract":"<div><div>Suppose <em>A</em> is an Azumaya algebra over a ring <em>R</em> and <em>σ</em> is an involution of <em>A</em> extending an order-2 automorphism <span><math><mi>λ</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math></span>. We say <em>σ</em> is <em>extraordinary</em> if there does not exist a Brauer-trivial Azumaya algebra <span><math><msub><mrow><mi>End</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>P</mi><mo>)</mo></math></span> over <em>R</em> carrying an involution <em>τ</em> so that <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span> and <span><math><mo>(</mo><msub><mrow><mi>End</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>P</mi><mo>)</mo><mo>,</mo><mi>τ</mi><mo>)</mo></math></span> become isomorphic over some faithfully flat extension of the fixed ring of <span><math><mi>λ</mi><mo>:</mo><mi>R</mi><mo>→</mo><mi>R</mi></math></span>. We give, for the first time, an example of such an algebra and involution. We do this by finding suitable cohomological obstructions and showing they do not always vanish.</div><div>We also give an example of a commutative ring <em>R</em> with involution <em>λ</em> so that the scheme-theoretic fixed locus <em>Z</em> of <span><math><mi>λ</mi><mo>:</mo><mi>Spec</mi><mspace></mspace><mi>R</mi><mo>→</mo><mi>Spec</mi><mspace></mspace><mi>R</mi></math></span> is disconnected, but such that every Azumaya algebra over <em>R</em> with involution extending <em>λ</em> is either orthogonal at every point of <em>Z</em>, or symplectic at every point of <em>Z</em>. No examples of this kind were previously known.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 256-279"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694951","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

Non-weight modules over the Lie (super)algebras related to the Virasoro algebra 与Virasoro代数相关的Lie（超）代数上的非权模

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.047

Yan-an Cai, Rencai Lü, Xinyue Wang

引用次数: 0

Reduction for (n + 2)-rigid subcategories in extriangulated categories 外三角化类别中（n + 2）-刚性子类别的约简

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.07.008

Mindy Y. Huerta

{"title":"Reduction for (n + 2)-rigid subcategories in extriangulated categories","authors":"Mindy Y. Huerta","doi":"10.1016/j.jalgebra.2025.07.008","DOIUrl":"10.1016/j.jalgebra.2025.07.008","url":null,"abstract":"<div><div>In this work we study how to extend the concept of <em>“reduction,”</em> given for rigid and functorially finite subcategories in an extriangulated category <span><math><mi>C</mi></math></span>, to <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></span>-rigid ones. We define the reduction of such subcategories as the intersection of orthogonal complements when certain orthogonal condition is satisfied and we prove that this reduction depends mainly on the subcategory itself beyond the type of extriangulated category for which belongs to. Specifically, we show that some results proven for Frobenius extriangulated categories can be carried to extriangulated categories in general. We also study some properties among we can mention: weakly idempotent completeness, existence of enough <span><math><mi>E</mi></math></span>-projectives and <span><math><mi>E</mi></math></span>-injectives, and conditions to be Frobenius. That generalization covers the usual case and, for the general case (for <span><math><mi>n</mi><mo>≥</mo><mn>0</mn></math></span>), we provide several examples. Finally, we extend a well-known result given for the reduction in stably 2-Calabi-Yau Frobenius extriangulated categories related with 2-cluster tilting subcategories.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 149-175"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686805","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 topological approach to key polynomials 关键多项式的拓扑方法

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.046

Enric Nart , Josnei Novacoski , Giulio Peruginelli

{"title":"A topological approach to key polynomials","authors":"Enric Nart , Josnei Novacoski , Giulio Peruginelli","doi":"10.1016/j.jalgebra.2025.06.046","DOIUrl":"10.1016/j.jalgebra.2025.06.046","url":null,"abstract":"<div><div>In this paper we present characterizations of the sets of key polynomials and abstract key polynomials for a valuation <em>μ</em> of <span><math><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, in terms of (ultrametric) balls in the algebraic closure <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span> of <em>K</em> with respect to <em>v</em>, a fixed extension of <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mo>|</mo><mi>K</mi></mrow></msub></math></span> to <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span>. In particular, we show that the ways of augmenting <em>μ</em>, in the sense of Mac Lane, are in one-to-one correspondence with the partition of a fixed closed ball <span><math><mi>B</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math></span> associated to <em>μ</em> into the disjoint union of open balls <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>∘</mo></mrow></msup><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>δ</mi><mo>)</mo></math></span>, modulo the action of the decomposition group of <em>v</em>. We also present a similar characterization for the set of limit key polynomials for an increasing family of valuations of <span><math><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 280-307"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694952","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

Orthogonal determinants of GLn(q) GLn(q)的正交决定因素

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-14 DOI: 10.1016/j.jalgebra.2025.07.005

Linda Hoyer

引用次数: 0

Groups with finitely many isomorphism classes of non-pronormal subgroups 具有有限多个非正规子群同构类的群

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-09 DOI: 10.1016/j.jalgebra.2025.07.004

Fausto De Mari

引用次数: 0