{"title":"Extension of Characters from the Radical of a Connected Lie Group to a One-Dimensional Pure Pseudorepresentation of the Group Revisited","authors":"A.I. Shtern","doi":"10.1134/S106192084010126","DOIUrl":null,"url":null,"abstract":"<p> Investigations concerning the extension of characters on normal subgroups to one-dimensional pure pseudorepresentations of the enveloping groups are continued. We prove necessary and sufficient conditions that an ordinary unitary character on the radical of a connected Lie group admits an extension to a one-dimensional pure pseudorepresentation of the group and prove the uniqueness of this pure pseudorepresentation if it exists. </p><p> <b> DOI</b> 10.1134/S106192084010126 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"146 - 148"},"PeriodicalIF":1.7000,"publicationDate":"2024-03-19","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://link.springer.com/article/10.1134/S106192084010126","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}
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Abstract
Investigations concerning the extension of characters on normal subgroups to one-dimensional pure pseudorepresentations of the enveloping groups are continued. We prove necessary and sufficient conditions that an ordinary unitary character on the radical of a connected Lie group admits an extension to a one-dimensional pure pseudorepresentation of the group and prove the uniqueness of this pure pseudorepresentation if it exists.
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.
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