Super 3-Lie Algebras Induced by Super Lie Algebras
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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.
KeywordsSuper Lie algebra Clifford algebra n-Lie algebra 3-Lie algebra Super n-Lie algebra Super 3-Lie algebra
Mathematics Subject ClassificationPrimary 17B56 Secondary 15A66
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- 1.Arnlind, J., Kitouni, A., Makhlouf, A., Silvestrov, S.: Structure and cohomology of 3-Lie algebras induced by Lie algebras. arXiv:1312.7599v