Czechoslovak Mathematical Journal

, Volume 64, Issue 4, pp 1019–1034 | Cite as

Some necessary and sufficient conditions for nilpotent n-Lie superalgebras

Article
First Online:
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Abstract

The paper studies nilpotent n-Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for n-Lie superalgebras which is a generalization of those for n-Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent n-Lie superalgebras and obtain several sufficient conditions for an n-Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the Jacobson radical.

Keywords

nilpotent n-Lie superalgebra Engel’s theorem S* algebra Frattini subalgebra 

MSC 2010

17B45 17B50 
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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Department of MathematicsJilin UniversityChangchun, JilinP.R. China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchun, JilinP.R. China

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