无连续性假设的可解连通李群的李氏定理

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2023-12-01 DOI:10.1134/s1061920823040180

{"title":"无连续性假设的可解连通李群的李氏定理","authors":"","doi":"10.1134/s1061920823040180","DOIUrl":null,"url":null,"abstract":" <h3>Abstract</h3> It is proved that if \\(G\\) is a connected solvable group and \\(\\pi\\) is a (not necessarily continuous) representation of \\(G\\) in a finite-dimensional vector space \\(E\\) , then there is a basis in \\(E\\) in which the matrices of the representation operators of \\(\\pi\\) have upper triangular form. The assertion is extended to connected solvable locally compact groups \\(G\\) having a connected normal subgroup for which the quotient group is a Lie group. DOI 10.1134/S1061920823040180 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lie’s Theorem for Solvable Connected Lie Groups Without the Continuity Assumption\",\"authors\":\"\",\"doi\":\"10.1134/s1061920823040180\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" <h3>Abstract</h3> It is proved that if \\\\(G\\\\) is a connected solvable group and \\\\(\\\\pi\\\\) is a (not necessarily continuous) representation of \\\\(G\\\\) in a finite-dimensional vector space \\\\(E\\\\) , then there is a basis in \\\\(E\\\\) in which the matrices of the representation operators of \\\\(\\\\pi\\\\) have upper triangular form. The assertion is extended to connected solvable locally compact groups \\\\(G\\\\) having a connected normal subgroup for which the quotient group is a Lie group. DOI 10.1134/S1061920823040180 \",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1134/s1061920823040180\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1061920823040180","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文证明，如果 \\(G\) 是一个连通可解群，并且 \\(\pi\) 是有限维向量空间 \\(E\) 中 \\(G\) 的一个（不一定连续的）表示，那么在 \\(E\) 中存在一个基，其中 \\(\pi\) 表示算子的矩阵具有上三角形式。这一论断被推广到具有连通法子群的连通可解局部紧凑群 \(G\)，其商群是一个李群。 doi 10.1134/s1061920823040180

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Lie’s Theorem for Solvable Connected Lie Groups Without the Continuity Assumption

Abstract

It is proved that if \(G\) is a connected solvable group and \(\pi\) is a (not necessarily continuous) representation of \(G\) in a finite-dimensional vector space \(E\) , then there is a basis in \(E\) in which the matrices of the representation operators of \(\pi\) have upper triangular form. The assertion is extended to connected solvable locally compact groups \(G\) having a connected normal subgroup for which the quotient group is a Lie group.

DOI 10.1134/S1061920823040180

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

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.