发布求助
文献互助 智能选刊 最新文献

Journal of Pure and Applied Algebra最新文献

筛选
英文 中文
The pro-nilpotent Lawrence-Krammer-Bigelow representation 亲零Lawrence-Krammer-Bigelow表示
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107952
Martin Palmer , Arthur Soulié
{"title":"The pro-nilpotent Lawrence-Krammer-Bigelow representation","authors":"Martin Palmer ,&nbsp;Arthur Soulié","doi":"10.1016/j.jpaa.2025.107952","DOIUrl":"10.1016/j.jpaa.2025.107952","url":null,"abstract":"<div><div>We construct a 3-variable enrichment of the Lawrence-Krammer-Bigelow (LKB) representation of the braid groups, which is the limit of a pro-nilpotent tower of representations having the original LKB representation as its bottom layer. We also construct analogous pro-nilpotent towers of representations of surface braid groups and loop braid groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107952"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738976","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
The isomorphism problem for rational group algebras of finite metacyclic groups 有限亚环群的有理群代数的同构问题
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107951
Àngel García-Blázquez, Ángel del Río
{"title":"The isomorphism problem for rational group algebras of finite metacyclic groups","authors":"Àngel García-Blázquez,&nbsp;Ángel del Río","doi":"10.1016/j.jpaa.2025.107951","DOIUrl":"10.1016/j.jpaa.2025.107951","url":null,"abstract":"<div><div>We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where the line separating positive and negative solutions to the Isomorphism Problem for group algebras lies.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107951"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683882","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
Deformations of unitary Howe dual pairs 幺正Howe对偶的变形
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107948
Dan Ciubotaru , Hendrik De Bie , Marcelo De Martino , Roy Oste
{"title":"Deformations of unitary Howe dual pairs","authors":"Dan Ciubotaru ,&nbsp;Hendrik De Bie ,&nbsp;Marcelo De Martino ,&nbsp;Roy Oste","doi":"10.1016/j.jpaa.2025.107948","DOIUrl":"10.1016/j.jpaa.2025.107948","url":null,"abstract":"<div><div>We study deformations of the Howe pairs <span><math><mo>(</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>U</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span> to the context of a rational Cherednik algebra <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>c</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> associated with a real reflection group <em>G</em> acting on a real vector space <em>E</em> of even dimension. For each pair, we show that the Lie (super)algebra structure of one partner is preserved under the deformation, which leads to a joint decomposition of the standard module or its tensor product with a spinor space. For the case where <em>E</em> is two-dimensional and <em>G</em> is a dihedral group, we provide complete descriptions for the deformed pair and the relevant joint-decomposition.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107948"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776895","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
Generalized (co)homology of symmetric quandles over homogeneous Beck modules 齐次Beck模上对称堆的广义（co）同调
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107956
Biswadeep Karmakar, Deepanshi Saraf, Mahender Singh
{"title":"Generalized (co)homology of symmetric quandles over homogeneous Beck modules","authors":"Biswadeep Karmakar,&nbsp;Deepanshi Saraf,&nbsp;Mahender Singh","doi":"10.1016/j.jpaa.2025.107956","DOIUrl":"10.1016/j.jpaa.2025.107956","url":null,"abstract":"<div><div>A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily oriented. In this paper, we introduce the category of symmetric quandle modules and prove that these modules completely determine the Beck modules in the category of symmetric quandles. Consequently, this establishes suitable coefficient objects for constructing appropriate (co)homology theories. We develop an extension theory of modules over symmetric quandles, and propose a generalized (co)homology theory for symmetric quandles with coefficients in a homogeneous Beck module, which also recovers the symmetric quandle (co)homology developed by Kamada and Oshiro (2010) <span><span>[16]</span></span>. Our constructions also apply to symmetric racks. We conclude by establishing an explicit isomorphism between the second cohomology of a symmetric quandle and the first cohomology of its associated group.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107956"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683880","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
Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line 具有最大皮卡数的一般类型曲面的无限多新序列收敛于塞韦里线
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107957
Nguyen Bin , Vicente Lorenzo
{"title":"Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line","authors":"Nguyen Bin ,&nbsp;Vicente Lorenzo","doi":"10.1016/j.jpaa.2025.107957","DOIUrl":"10.1016/j.jpaa.2025.107957","url":null,"abstract":"<div><div>Examples of algebraic surfaces of general type with maximal Picard number are not abundant in the literature. Moreover, most known examples either possess low invariants, lie near the Noether line <span><math><msup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>2</mn><mi>χ</mi><mo>−</mo><mn>6</mn></math></span> or are somewhat scattered. A notable exception is Persson's sequence of double covers of the projective plane with maximal Picard number, whose invariants converge to the Severi line <span><math><msup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>4</mn><mi>χ</mi></math></span>. This note is devoted to the construction of infinitely many new sequences of surfaces of general type with maximal Picard number whose invariants converge to the Severi line.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107957"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696108","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 based rings of two-sided cells in an affine Weyl group of type B˜3, III B ~ 3，iii型仿射Weyl群中双面细胞的基环
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107950
Yannan Qiu
{"title":"The based rings of two-sided cells in an affine Weyl group of type B˜3, III","authors":"Yannan Qiu","doi":"10.1016/j.jpaa.2025.107950","DOIUrl":"10.1016/j.jpaa.2025.107950","url":null,"abstract":"<div><div>We compute the based ring of the two-sided cell corresponding to the unipotent class in <span><math><mi>S</mi><msub><mrow><mi>p</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math></span> with Jordan blocks (2211). The result also verifies Lusztig's conjecture on the structure of the based rings of the two-sided cells of an affine Weyl group.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107950"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738975","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
Fiber criteria for flatness and homomorphisms of flat affine group schemes 平面仿射群方案的平面性和同态的纤维判据
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-19 DOI: 10.1016/j.jpaa.2025.107949
Phùng Hô Hai , Hop D. Nguyen , João Pedro dos Santos
{"title":"Fiber criteria for flatness and homomorphisms of flat affine group schemes","authors":"Phùng Hô Hai ,&nbsp;Hop D. Nguyen ,&nbsp;João Pedro dos Santos","doi":"10.1016/j.jpaa.2025.107949","DOIUrl":"10.1016/j.jpaa.2025.107949","url":null,"abstract":"<div><div>A very useful result concerning flatness in Algebraic Geometry is EGA's “fiber” criterion. We propose similar fiber criteria to verify flatness of a module while avoiding “finiteness” assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107949"},"PeriodicalIF":0.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683881","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 associated graded algebras of Brauer graph algebras II: Infinite representation type Brauer图代数的相关分级代数II：无限表示型
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-18 DOI: 10.1016/j.jpaa.2025.107954
Jing Guo , Yuming Liu , Yu Ye
{"title":"The associated graded algebras of Brauer graph algebras II: Infinite representation type","authors":"Jing Guo ,&nbsp;Yuming Liu ,&nbsp;Yu Ye","doi":"10.1016/j.jpaa.2025.107954","DOIUrl":"10.1016/j.jpaa.2025.107954","url":null,"abstract":"<div><div>Let <em>G</em> be a Brauer graph and <em>A</em> the associated Brauer graph algebra. Denote by <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> the graded algebra associated with the radical filtration of <em>A</em>. The question when <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is of finite representation type was answered in a previous paper. In the present paper, we characterize when <span><math><mrow><mi>gr</mi></mrow><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is domestic in terms of the associated Brauer graph <em>G</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107954"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704492","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 derivations of free algebras over operads and the generalized divergence 自由代数在操作数上的导数与广义散度
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-18 DOI: 10.1016/j.jpaa.2025.107947
Geoffrey Powell
{"title":"On derivations of free algebras over operads and the generalized divergence","authors":"Geoffrey Powell","doi":"10.1016/j.jpaa.2025.107947","DOIUrl":"10.1016/j.jpaa.2025.107947","url":null,"abstract":"<div><div>For <span><math><mi>O</mi></math></span> a reduced operad, a generalized divergence from the derivations of a free <span><math><mi>O</mi></math></span>-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the associative operad, to the double divergence of Alekseev, Kawazumi, Kuno and Naef. The generalized divergence is shown to be a 1-cocycle for the usual Lie algebra structure on derivations. These results place the previous constructions into a unified framework; moreover, they are natural with respect to the operad.</div><div>An important new ingredient is the use of naturality with respect to the category of finite-rank free modules and split monomorphisms over a commutative ring <em>R</em>. This allows the notion of torsion for such functors to be exploited.</div><div>Supposing that the ring <em>R</em> is a PID and that the operad <span><math><mi>O</mi></math></span> is binary, the main result relates the kernel of the generalized divergence to the sub Lie algebra of the Lie algebra of derivations that is generated by the elements of degree one with respect to the grading induced by arity.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107947"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683879","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 representation embedding for algebras of infinite type 无限型代数的表示嵌入
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-03-17 DOI: 10.1016/j.jpaa.2025.107955
R. Bautista , E. Pérez , L. Salmerón
{"title":"A representation embedding for algebras of infinite type","authors":"R. Bautista ,&nbsp;E. Pérez ,&nbsp;L. Salmerón","doi":"10.1016/j.jpaa.2025.107955","DOIUrl":"10.1016/j.jpaa.2025.107955","url":null,"abstract":"<div><div>We show that for any finite-dimensional algebra Λ of infinite representation type, over a perfect field, there is a bounded principal ideal domain Γ and a representation embedding from <span><math><mi>Γ</mi><mtext>-</mtext><mrow><mi>mod</mi></mrow></math></span> into <span><math><mi>Λ</mi><mtext>-</mtext><mrow><mi>mod</mi></mrow></math></span>. As an application, we prove a variation of the second Brauer-Thrall conjecture: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107955"},"PeriodicalIF":0.7,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759662","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信