算子代数酉群中的极大离散子群

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-06-14 DOI:10.3842/sigma.2022.052

V. Alekseev, A. Thom

{"title":"算子代数酉群中的极大离散子群","authors":"V. Alekseev, A. Thom","doi":"10.3842/sigma.2022.052","DOIUrl":null,"url":null,"abstract":". We show that if a group G is mixed-identity-free, then the projective unitary group of its group von Neumann algebra contains a maximal discrete subgroup containing G . The proofs are elementary and make use of free probability theory. In addition, we clarify the situation for C ∗ -algebras.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Maximal Discrete Subgroups in Unitary Groups of Operator Algebras\",\"authors\":\"V. Alekseev, A. Thom\",\"doi\":\"10.3842/sigma.2022.052\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We show that if a group G is mixed-identity-free, then the projective unitary group of its group von Neumann algebra contains a maximal discrete subgroup containing G . The proofs are elementary and make use of free probability theory. In addition, we clarify the situation for C ∗ -algebras.\",\"PeriodicalId\":49453,\"journal\":{\"name\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3842/sigma.2022.052\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3842/sigma.2022.052","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

.我们证明了如果群G是无混合恒等式的，则其群von Neumann代数的投影酉群包含一个包含G的极大离散子群。这些证明是初等的，并利用了自由概率论。此外，我们还阐明了C*-代数的情形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Maximal Discrete Subgroups in Unitary Groups of Operator Algebras

. We show that if a group G is mixed-identity-free, then the projective unitary group of its group von Neumann algebra contains a maximal discrete subgroup containing G . The proofs are elementary and make use of free probability theory. In addition, we clarify the situation for C ∗ -algebras.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.