Omni-Lie superalgebras and Lie 2-superalgebras

Abstract

We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space.

Keywords

Lie 2-superalgebra / Leibniz superalgebra / Dirac structure

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Higher Education Press and Springer-Verlag Berlin Heidelberg