Algebras and Representation Theory最新文献_第9页

Module Categories of Small Radical Nilpotency 小根幂零的模范畴

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-24 DOI: 10.1007/s10468-023-10211-3

Shiping Liu, Youqi Yin

引用次数: 0

Wild Local Structures of Automorphic Lie Algebras 自同构李代数的Wild局部结构

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-20 DOI: 10.1007/s10468-023-10208-y

Drew Damien Duffield, Vincent Knibbeler, Sara Lombardo

引用次数: 0

Classifying Recollements of Derived Module Categories for Derived Discrete Algebras 导出离散代数的导出模范畴的分类集合

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-12 DOI: 10.1007/s10468-023-10220-2

Xiuli Bian

引用次数: 0

Topologically Semiperfect Topological Rings 拓扑半完全拓扑环

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-10 DOI: 10.1007/s10468-023-10217-x

Leonid Positselski, Jan Šťovíček

{"title":"Topologically Semiperfect Topological Rings","authors":"Leonid Positselski, Jan Šťovíček","doi":"10.1007/s10468-023-10217-x","DOIUrl":"10.1007/s10468-023-10217-x","url":null,"abstract":"<div><p>We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a module, endowed with the finite topology, is topologically semiperfect if and only if the module is decomposable as an (infinite) direct sum of modules with local endomorphism rings. Then we study structural properties of topologically semiperfect topological rings and prove that their topological Jacobson radicals are strongly closed and the related topological quotient rings are topologically semisimple. For the endomorphism ring of a direct sum of modules with local endomorphism rings, the topological Jacobson radical is described explicitly as the set of all matrices of nonisomorphisms. Furthermore, we prove that, over a topologically semiperfect topological ring, all finitely generated discrete modules have projective covers in the category of modules, while all lattice-finite contramodules have projective covers in both the categories of modules and contramodules. We also show that the topological Jacobson radical of a topologically semiperfect topological ring is equal to the closure of the abstract Jacobson radical, and present a counterexample demonstrating that the topological Jacobson radical can be strictly larger than the abstract one. Finally, we discuss the problem of lifting idempotents modulo the topological Jacobson radical and the structure of projective contramodules for topologically semiperfect topological rings.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"245 - 278"},"PeriodicalIF":0.5,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-023-10217-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46266389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Epimorphic Quantum Subgroups and Coalgebra Codominions 外纯量子子群与协代数共域

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-08 DOI: 10.1007/s10468-023-10219-9

Alexandru Chirvasitu

{"title":"Epimorphic Quantum Subgroups and Coalgebra Codominions","authors":"Alexandru Chirvasitu","doi":"10.1007/s10468-023-10219-9","DOIUrl":"10.1007/s10468-023-10219-9","url":null,"abstract":"<div><p>We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a) representation-theoretic characterizations of monomorphisms in all of these categories that when the Hopf algebras in question are commutative specialize back to the familiar necessary and sufficient conditions (due to Bien-Borel) that a linear algebraic subgroup be epimorphically embedded; (b) the fact that a morphism in the category of (cocommutative) coalgebras, (cocommutative) bialgebras, and a host of categories of Hopf algebras has the same codominion in any of these categories which contain it; (c) the invariance of the Hopf algebra or bialgebra (co)dominion construction under field extension, again mimicking the well-known corresponding algebraic-group result; (d) the fact that surjections of coalgebras, bialgebras or Hopf algebras are regular epimorphisms (i.e. coequalizers) provided the codomain is cosemisimple; (e) in particular, the fact that embeddings of compact quantum groups are equalizers in the category thereof, generalizing analogous results on (plain) compact groups; (f) coalgebra-limit preservation results for scalar-extension functors (e.g. extending scalars along a field extension <span>(Bbbk le Bbbk ')</span> is a right adjoint on the category of <span>(Bbbk )</span>-coalgebras).</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"219 - 244"},"PeriodicalIF":0.5,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47951585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Stable Unital Bases, Hyperfocal Subalgebras and Basic Morita Equivalences 稳定酉基、超焦子代数和基本Morita等价

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-03 DOI: 10.1007/s10468-023-10216-y

Tiberiu Coconeţ, Constantin-Cosmin Todea

引用次数: 0

A Generalization of the Correspondences Between Quasi-Hereditary Algebras and Directed Bocses 拟遗传代数与有向Boces对应关系的推广

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-07-03 DOI: 10.1007/s10468-023-10212-2

Yuichiro Goto

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引用次数: 0

Finite GK-Dimensional Nichols Algebras Over the Infinite Dihedral Group 无限二面体群上的有限GK维Nichols代数

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-06-29 DOI: 10.1007/s10468-023-10213-1

Yongliang Zhang

引用次数: 0

Modular Products and Modules for Finite Groups 模积与有限群的模

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2023-06-26 DOI: 10.1007/s10468-023-10210-4

John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun

引用次数: 0

On the Ideals of Ultragraph Leavitt Path Algebras 关于超图莱维特路径代数的理想