Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 9–16 | Cite as

Super 3-Lie Algebras Induced by Super Lie Algebras



We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a Clifford algebra with even number of generators and making use of a matrix representation of this super Lie algebra given by a supermodule of spinors we construct a series of super 3-Lie algebras labeled by positive even integers.


Super Lie algebra Clifford algebra n-Lie algebra 3-Lie algebra Super n-Lie algebra Super 3-Lie algebra 

Mathematics Subject Classification

Primary 17B56 Secondary 15A66 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TartuTartuEstonia

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