Completable nilpotent Lie superalgebras

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• 作者：Mingzhong Wu (1) (2)
  
  1. Chern Institute of Mathematics and LPMC ; Nankai University ; Tianjin ; 300071 ; China
  2. Department of Mathematics ; China West Normal University ; Nanchong ; 637002 ; China
  
• 关键词：Filiform Lie superalgebra ; Heisenberg superalgebra ; completable nilpotent Lie superalgebra ; maximal torus ; complete Lie superalgebra ; 17B30 ; 17B40
• 刊名：Frontiers of Mathematics in China
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：10
• 期：3
• 页码：697-713
• 全文大小：168 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

We discuss a class of filiform Lie superalgebras L n,m . From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of \(Der_{\bar 0} \left( {L^{n,m} } \right)\) and \(Der_{\bar 1} \left( {L^{n,m} } \right)\) . By computing a maximal torus on each L n,m , we show that L n,m are completable nilpotent Lie superalgebras. We also view L n,m as Lie algebras, prove that L n,m are of maximal rank, and show that L n,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.