{"title":"On the structure of low-dimensional Leibniz algebras: some revision","authors":"L. A. Kurdachenko, O. Pypka, I. Subbotin","doi":"10.12958/adm2036","DOIUrl":null,"url":null,"abstract":"Let L be an algebra over a field F with the binary operations + and [·,·]. Then L is called a left Leibniz algebra if [[a,b],c]=[a,[b,c]]−[b,[a,c]] for all a, b, c ∈ L. We describe the inner structure of left Leibniz algebras having dimension 3.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm2036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 6
Abstract
Let L be an algebra over a field F with the binary operations + and [·,·]. Then L is called a left Leibniz algebra if [[a,b],c]=[a,[b,c]]−[b,[a,c]] for all a, b, c ∈ L. We describe the inner structure of left Leibniz algebras having dimension 3.
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