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Abelianization of SL2 over Dedekind domains of arithmetic type 算术型Dedekind域上SL2的阿贝尔化
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.08.046
Behrooz Mirzaii, Bruno R. Ramos, Thiago Verissimo
{"title":"Abelianization of SL2 over Dedekind domains of arithmetic type","authors":"Behrooz Mirzaii,&nbsp;Bruno R. Ramos,&nbsp;Thiago Verissimo","doi":"10.1016/j.jalgebra.2025.08.046","DOIUrl":"10.1016/j.jalgebra.2025.08.046","url":null,"abstract":"<div><div>We determine the exact group structure of the abelianization of <span><math><msub><mrow><mtext>SL</mtext></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, in which <em>A</em> is a Dedekind domain of arithmetic type with infinitely many units. In particular, our results show that <span><math><msub><mrow><mtext>SL</mtext></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><mtext>ab</mtext></mrow></msup></math></span> is finite, with exponent dividing 12 when <span><math><mtext>char</mtext><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, and dividing 6 when <span><math><mtext>char</mtext><mo>(</mo><mi>A</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></math></span>. As illustrative examples, we compute <span><math><msub><mrow><mtext>SL</mtext></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><mtext>ab</mtext></mrow></msup></math></span> explicitly for instances where <em>A</em> is the ring of integers of a real quadratic field or a cyclotomic extension.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 1-20"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145278406","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
Some semidirect products of skew braces arising in Hopf-Galois theory Hopf-Galois理论中斜撑的半直积
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.10.004
Paul J. Truman
{"title":"Some semidirect products of skew braces arising in Hopf-Galois theory","authors":"Paul J. Truman","doi":"10.1016/j.jalgebra.2025.10.004","DOIUrl":"10.1016/j.jalgebra.2025.10.004","url":null,"abstract":"<div><div>We classify skew braces that are the semidirect product of an ideal and a left ideal. As a consequence, given a Galois extension of fields <span><math><mi>L</mi><mo>/</mo><mi>K</mi></math></span> whose Galois group is the semidirect product of a normal subgroup <em>A</em> and a subgroup <em>B</em>, we classify the Hopf-Galois structures on <span><math><mi>L</mi><mo>/</mo><mi>K</mi></math></span> that realize <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> via a normal Hopf subalgebra and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>B</mi></mrow></msup></math></span> via a Hopf subalgebra. We show that the Hopf algebra giving such a Hopf-Galois structure is the smash product of these Hopf subalgebras, and use this description to study generalized normal basis generators and questions of integral module structure in extensions of local fields.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 825-850"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321296","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
Lifting generators in connected Lie groups 连接李群中的起重发电机
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.09.022
Tal Cohen , Itamar Vigdorovich
{"title":"Lifting generators in connected Lie groups","authors":"Tal Cohen ,&nbsp;Itamar Vigdorovich","doi":"10.1016/j.jalgebra.2025.09.022","DOIUrl":"10.1016/j.jalgebra.2025.09.022","url":null,"abstract":"<div><div>Given an epimorphism between topological groups <span><math><mi>f</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span>, when can a generating set of <em>H</em> be lifted to a generating set of <em>G</em>?</div><div>We show that for connected Lie groups the problem is fundamentally abelian: generators can be lifted if and only if they can be lifted in the induced map between the abelianisations (assuming the number of generators is at least the minimal number of generators of <em>G</em>). As a consequence, we deduce that connected perfect Lie groups satisfy the Gaschütz lemma: generating sets of quotients can always be lifted. If the Lie group is not perfect, this may fail. The extent to which a group fails to satisfy the Gaschütz lemma is measured by its <em>Gaschütz rank</em>, which we bound for all connected Lie groups, and compute exactly in most cases. Additionally, we compute the maximal size of an irredundant generating set of connected abelian Lie groups, and discuss connections between such generation problems with the Wiegold conjecture.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 156-188"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334833","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 a question by Roggenkamp about group algebras 关于罗根坎普关于群代数的一个问题
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.09.014
Dylan Johnston, Dmitriy Rumynin
{"title":"On a question by Roggenkamp about group algebras","authors":"Dylan Johnston,&nbsp;Dmitriy Rumynin","doi":"10.1016/j.jalgebra.2025.09.014","DOIUrl":"10.1016/j.jalgebra.2025.09.014","url":null,"abstract":"<div><div>We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a conjecture, which extends the criterion.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 776-791"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321294","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 a conjecture of Zhao related to standard relations among cyclotomic multiple zeta values 关于切环多重zeta值之间标准关系的赵氏猜想
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.10.003
Henrik Bachmann, Khalef Yaddaden
{"title":"On a conjecture of Zhao related to standard relations among cyclotomic multiple zeta values","authors":"Henrik Bachmann,&nbsp;Khalef Yaddaden","doi":"10.1016/j.jalgebra.2025.10.003","DOIUrl":"10.1016/j.jalgebra.2025.10.003","url":null,"abstract":"<div><div>We provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence between two schemes attached to a finite abelian group <em>G</em>. In particular, when <em>G</em> is the group of roots of unity, these schemes describe the standard relations among cyclotomic multiple zeta values.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 21-58"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334825","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 rigid varieties isogenous to a product of curves 在刚体变异上，等值于曲线的乘积
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.09.016
Federico Fallucca , Christian Gleissner , Noah Ruhland
{"title":"On rigid varieties isogenous to a product of curves","authors":"Federico Fallucca ,&nbsp;Christian Gleissner ,&nbsp;Noah Ruhland","doi":"10.1016/j.jalgebra.2025.09.016","DOIUrl":"10.1016/j.jalgebra.2025.09.016","url":null,"abstract":"<div><div>In this note, we study rigid complex manifolds that are realized as quotients of a product of curves by a free action of a finite group. They serve as higher-dimensional analogues of Beauville surfaces. Using uniformization, we outline the theory to characterize these manifolds through specific combinatorial data associated with the group under the assumption that the action is diagonal and the manifold is of general type. This leads to the notion of a <em>n</em>-fold Beauville structure. We define an action on the set of all <em>n</em>-fold Beauville structures of a given finite group that allows us to distinguish the biholomorphism classes of the underlying rigid manifolds. As an application, we give a classification of these manifolds with group <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> in the three dimensional case and prove that this is the smallest possible group that allows a rigid, free and diagonal action on a product of three curves. In addition, we provide the classification of rigid 3-folds <em>X</em> given by a group acting faithfully on each factor for any value of the holomorphic Euler number <span><math><mi>χ</mi><mo>(</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo><mo>≥</mo><mo>−</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 393-419"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334826","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
The Newton-Puiseux algorithm and effective algebraic series 牛顿-普塞算法和有效代数级数
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.09.027
Manfred Buchacher
{"title":"The Newton-Puiseux algorithm and effective algebraic series","authors":"Manfred Buchacher","doi":"10.1016/j.jalgebra.2025.09.027","DOIUrl":"10.1016/j.jalgebra.2025.09.027","url":null,"abstract":"<div><div>We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series. Furthermore, we discuss how to derive information about the support of an algebraic series. Based thereon, we show how to identify the polynomial and rational solutions of a polynomial equation.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 284-306"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334030","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
Lie conformal superalgebras of rank (2 + 1) 秩为（2 + 1）的李共形超代数
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.08.045
Jinrong Wang, Xiaoqing Yue
{"title":"Lie conformal superalgebras of rank (2 + 1)","authors":"Jinrong Wang,&nbsp;Xiaoqing Yue","doi":"10.1016/j.jalgebra.2025.08.045","DOIUrl":"10.1016/j.jalgebra.2025.08.045","url":null,"abstract":"<div><div>In this paper, Lie conformal superalgebras of rank <span><math><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></math></span> are completely classified (up to isomorphism) and their automorphism groups are determined. Furthermore, we give the classification of finite irreducible conformal modules over them and their actions are explicitly described. In addition, we introduce several new infinite-dimensional Lie superalgebras associated with previously constructed Lie conformal superalgebras. We also prove that all finite nontrivial irreducible conformal modules over a class of Lie conformal superalgebras must be of rank one.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 116-155"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334832","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
Boolean Schubert structure coefficients 布尔舒伯特结构系数
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-10 DOI: 10.1016/j.jalgebra.2025.09.024
Yibo Gao , Hai Zhu
{"title":"Boolean Schubert structure coefficients","authors":"Yibo Gao ,&nbsp;Hai Zhu","doi":"10.1016/j.jalgebra.2025.09.024","DOIUrl":"10.1016/j.jalgebra.2025.09.024","url":null,"abstract":"<div><div>The Schubert problem asks for combinatorial models to compute structure constants of the cohomology ring with respect to Schubert classes and has been an important open problem in algebraic geometry and combinatorics that guided fruitful research for decades. In this paper, we provide an explicit formula for the (equivariant) Schubert structure constants <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>u</mi><mi>v</mi></mrow><mrow><mi>w</mi></mrow></msubsup></math></span> across all Lie types when the elements <span><math><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi></math></span> are boolean. In particular, in type <em>A</em>, all Schubert structure constants on boolean elements are either 0 or 1.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"688 ","pages":"Pages 344-362"},"PeriodicalIF":0.8,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334824","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
Profinite groups with complemented closed subgroups 具有补闭子群的无限群
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2025-10-06 DOI: 10.1016/j.jalgebra.2025.09.013
Gustavo A. Fernández-Alcober, Giulia Sabatino
{"title":"Profinite groups with complemented closed subgroups","authors":"Gustavo A. Fernández-Alcober,&nbsp;Giulia Sabatino","doi":"10.1016/j.jalgebra.2025.09.013","DOIUrl":"10.1016/j.jalgebra.2025.09.013","url":null,"abstract":"<div><div>A group <em>G</em> is said to be a <em>C</em>-group if every subgroup <em>H</em> has a permutable complement, i.e. if there exists a subgroup <em>K</em> of <em>G</em> such that <span><math><mi>G</mi><mo>=</mo><mi>H</mi><mi>K</mi></math></span> and <span><math><mi>H</mi><mo>∩</mo><mi>K</mi><mo>=</mo><mn>1</mn></math></span>. In this paper, we study the profinite counterpart of this concept. We say that a profinite group <em>G</em> is profinite-<em>C</em> if every closed subgroup admits a closed permutable complement. We first give some equivalent variants of this condition and then we determine the structure of profinite-<em>C</em> groups: they are the semidirect products <span><math><mi>G</mi><mo>=</mo><mi>B</mi><mo>⋉</mo><mi>A</mi></math></span> of two closed subgroups <span><math><mi>A</mi><mo>=</mo><msub><mrow><mi>Cr</mi></mrow><mrow><mi>i</mi><mo>∈</mo><mi>I</mi></mrow></msub><mspace></mspace><mspace></mspace><mo>〈</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>〉</mo></math></span> and <span><math><mi>B</mi><mo>=</mo><msub><mrow><mi>Cr</mi></mrow><mrow><mi>j</mi><mo>∈</mo><mi>J</mi></mrow></msub><mspace></mspace><mspace></mspace><mo>〈</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>〉</mo></math></span> that are cartesian products of cyclic groups of prime order, and with every <span><math><mo>〈</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>〉</mo></math></span> normal in <em>G</em>. Finally, we show that a profinite-<em>C</em> group is a <em>C</em>-group if and only if it is torsion and <span><math><mo>|</mo><mi>G</mi><mo>:</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo><mover><mrow><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mo>‾</mo></mover><mo>|</mo><mo>&lt;</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"687 ","pages":"Pages 763-775"},"PeriodicalIF":0.8,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268104","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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