{"title":"Finite W-algebras associated to truncated current Lie algebras","authors":"Xiao He","doi":"10.3336/gm.57.1.02","DOIUrl":null,"url":null,"abstract":"Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \\(s\\ell_2\\) case.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.57.1.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \(s\ell_2\) case.
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