Journal of Algebra最新文献_第3页

Extending structures for dendriform algebras 树枝状代数的扩展结构

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-15 DOI: 10.1016/j.jalgebra.2024.09.025

Yuanyuan Zhang, Junwen Wang

引用次数: 0

Unramified Brauer group of quotient spaces by finite groups 有限群商数空间的非ramified Brauer 群

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-15 DOI: 10.1016/j.jalgebra.2024.10.006

Andrew Kresch , Yuri Tschinkel

引用次数: 0

Noncommutative differential geometry on crossed product algebras 交叉积代数上的非交换微分几何

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-15 DOI: 10.1016/j.jalgebra.2024.10.007

Andrea Sciandra , Thomas Weber

{"title":"Noncommutative differential geometry on crossed product algebras","authors":"Andrea Sciandra , Thomas Weber","doi":"10.1016/j.jalgebra.2024.10.007","DOIUrl":"10.1016/j.jalgebra.2024.10.007","url":null,"abstract":"<div><div>We provide a differential structure on arbitrary cleft extensions <math><mi>B</mi><mo>:</mo><mo>=</mo><msup><mrow><mi>A</mi></mrow><mrow><mrow><mi>co</mi></mrow><mi>H</mi></mrow></msup><mo>⊆</mo><mi>A</mi></math> for an H-comodule algebra A. This is achieved by constructing a covariant calculus on the corresponding crossed product algebra <math><mi>B</mi><msub><mrow><mi>#</mi></mrow><mrow><mi>σ</mi></mrow></msub><mi>H</mi></math> from the data of a bicovariant calculus on the structure Hopf algebra H and a calculus on the base algebra B, which is compatible with the 2-cocycle and measure of the crossed product. The result is a quantum principal bundle with canonical strong connection and we describe the induced bimodule covariant derivatives on associated bundles of the crossed product. All results specialize to trivial extensions and smash product algebras B#H and we give a characterization of the smash product calculus in terms of the differentials of the cleaving map <math><mi>j</mi><mo>:</mo><mi>H</mi><mo>→</mo><mi>A</mi></math> and the inclusion <math><mi>B</mi><mo>↪</mo><mi>A</mi></math>. The construction is exemplified for pointed Hopf algebras. In particular, the case of Radford Hopf algebras <math><msub><mrow><mi>H</mi></mrow><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></msub></math> is spelled out in detail.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529834","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

Invariants of r-spin TQFTs and non-semisimplicity r-自旋 TQFT 的不变式与非半简性

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-15 DOI: 10.1016/j.jalgebra.2024.08.039

Nils Carqueville , Ehud Meir , Lóránt Szegedy

引用次数: 0

Subalgebras of octonion algebras 八元数子代数

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.10.004

Norbert Knarr, Markus J. Stroppel

引用次数: 0

Relative monadicity 相对单一性

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.08.040

Nathanael Arkor , Dylan McDermott

{"title":"Relative monadicity","authors":"Nathanael Arkor , Dylan McDermott","doi":"10.1016/j.jalgebra.2024.08.040","DOIUrl":"10.1016/j.jalgebra.2024.08.040","url":null,"abstract":"<div><div>We establish a relative monadicity theorem for relative monads with dense roots in a virtual equipment, specialising to a relative monadicity theorem for enriched relative monads. In particular, for a dense <figure><img></figure>-functor <math><mi>j</mi><mo>:</mo><mi>A</mi><mo>→</mo><mi>E</mi></math>, a <figure><img></figure>-functor <math><mi>r</mi><mo>:</mo><mi>D</mi><mo>→</mo><mi>E</mi></math> is j-monadic if and only if r admits a left j-relative adjoint and creates j-absolute colimits. This provides a refinement of the classical monadicity theorem – characterising those categories whose objects are given by those of E equipped with algebraic structure – in which the arities of the algebraic operations are valued in A. In particular, when <math><mi>j</mi><mo>=</mo><mn>1</mn></math>, we recover a formal monadicity theorem. Furthermore, we examine the interaction between the pasting law for relative adjunctions and relative monadicity. As a consequence, we derive necessary and sufficient conditions for the (j-relative) monadicity of the composite of a <figure><img></figure>-functor with a (j-relatively) monadic <figure><img></figure>-functor.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442427","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

Equivalence between invariance conjectures for parabolic Kazhdan-Lusztig polynomials 抛物线卡兹丹-卢兹蒂格多项式不变性猜想之间的等价性

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.09.026

Paolo Sentinelli

引用次数: 0

A categorification of cluster algebras of type B and C through symmetric quivers 通过对称四元组对 B 型和 C 型簇代数进行分类

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.09.015

Azzurra Ciliberti

引用次数: 0

Pro-C RAAGs Pro-C RAAGs

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.09.030

Montserrat Casals-Ruiz , Matteo Pintonello , Pavel Zalesskii

{"title":"Pro-C RAAGs","authors":"Montserrat Casals-Ruiz , Matteo Pintonello , Pavel Zalesskii","doi":"10.1016/j.jalgebra.2024.09.030","DOIUrl":"10.1016/j.jalgebra.2024.09.030","url":null,"abstract":"<div><div>Let <math><mi>C</mi></math> be a class of finite groups closed under taking subgroups, quotients, and extensions with abelian kernel. The right-angled Artin pro-<math><mi>C</mi></math> group <math><msub><mrow><mi>G</mi></mrow><mrow><mi>Γ</mi></mrow></msub></math> (pro-<math><mi>C</mi></math> RAAG for short) is the pro-<math><mi>C</mi></math> completion of the right-angled Artin group <math><mi>G</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math> associated with the finite simplicial graph Γ.</div><div>In the first part, we describe structural properties of pro-<math><mi>C</mi></math> RAAGs. Among others, we describe the centraliser of an element and show that pro-<math><mi>C</mi></math> RAAGs satisfy the Tits' alternative, that standard subgroups are isolated, and that 2-generated pro-p subgroups of pro-<math><mi>C</mi></math> RAAGs are either free pro-p or free abelian pro-p.</div><div>In the second part, we characterise splittings of pro-<math><mi>C</mi></math> RAAGs in terms of the defining graph. More precisely, we prove that a pro-<math><mi>C</mi></math> RAAG <math><msub><mrow><mi>G</mi></mrow><mrow><mi>Γ</mi></mrow></msub></math> splits as a non-trivial direct product if and only if Γ is a join and it splits over an abelian pro-<math><mi>C</mi></math> group if and only if a connected component of Γ is a complete graph or it has a complete disconnecting subgraph. We then use this characterisation to describe an abelian JSJ decomposition of a pro-<math><mi>C</mi></math> RAAG, in the sense of Guirardel and Levitt [9].</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529835","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

Galois theory and homology in quasi-abelian functor categories 准阿贝尔函数范畴中的伽罗瓦理论和同源性

IF 0.8 2区数学

Journal of Algebra Pub Date : 2024-10-11 DOI: 10.1016/j.jalgebra.2024.09.031

Nadja Egner

{"title":"Galois theory and homology in quasi-abelian functor categories","authors":"Nadja Egner","doi":"10.1016/j.jalgebra.2024.09.031","DOIUrl":"10.1016/j.jalgebra.2024.09.031","url":null,"abstract":"<div><div>Given a finite category <math><mi>T</mi></math>, we consider the functor category <math><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></math>, where <math><mi>A</mi></math> can be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as the categories of torsion(-free) abelian groups, topological abelian groups, locally compact abelian groups, Banach spaces and Fréchet spaces. In this situation, the categories of various internal categorical structures in <math><mi>A</mi></math>, such as the categories of internal n-fold groupoids, are equivalent to functor categories <math><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></math> for a suitable category <math><mi>T</mi></math>. For a replete full subcategory <math><mi>S</mi></math> of <math><mi>T</mi></math>, we define <math><mi>F</mi></math> to be the full subcategory of <math><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></math> whose objects are given by the functors <math><mi>F</mi><mo>:</mo><mi>T</mi><mo>→</mo><mi>A</mi></math> with <math><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>=</mo><mn>0</mn></math> for all <math><mi>T</mi><mo>∉</mo><mi>S</mi></math>. We prove that <math><mi>F</mi></math> is a torsion-free Birkhoff subcategory of <math><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></math>. This allows us to study (higher) central extensions from categorical Galois theory in <math><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></math> with respect to <math><mi>F</mi></math> and generalized Hopf formulae for homology.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442411","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