{"title":"On representation theory of Lie triple systems","authors":"A. Alshahrani","doi":"10.12988/ija.2022.91720","DOIUrl":null,"url":null,"abstract":"The present work concerns certain aspects of Lie algebras, Lie triple systems and Jordan triple systems. We summarize the latest results on the universal enveloping algebras of Lie algebras and Lie triple systems. In particular, we study a Casimir element as the element in the center of the universal enveloping algebras. Using this element, we characterize the semi-simple Lie triple systems among the quadratic Lie triple systems. We define Jordan’s triple systems relationship with algebras and Lie algebras. Finally, we prove some theorems, examples and facts on all of the above. Mathematics Subject Classification: 17C50, 17B60, 17B20, 17B05","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Algebra and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/ija.2022.91720","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
The present work concerns certain aspects of Lie algebras, Lie triple systems and Jordan triple systems. We summarize the latest results on the universal enveloping algebras of Lie algebras and Lie triple systems. In particular, we study a Casimir element as the element in the center of the universal enveloping algebras. Using this element, we characterize the semi-simple Lie triple systems among the quadratic Lie triple systems. We define Jordan’s triple systems relationship with algebras and Lie algebras. Finally, we prove some theorems, examples and facts on all of the above. Mathematics Subject Classification: 17C50, 17B60, 17B20, 17B05
期刊介绍：
The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.
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