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Omni-Lie Superalgebras and Lie 2-superalgebras

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

preprint2013arXivOpen access
Tao ZhangZhangju Liu
math-phmath.MPmath.RA
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Tao ZhangZhangju Liu

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