{"title":"Graded modules over simple Lie algebras","authors":"Y. Bahturin, M. Kochetov, Abdallah Shihadeh","doi":"10.15446/recolma.v53nsupl.84006","DOIUrl":null,"url":null,"abstract":"The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/recolma.v53nsupl.84006","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Colombiana de Matematicas","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15446/recolma.v53nsupl.84006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.
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