1301.2839 (Tao Zhang et al.)

Omni-Lie Superalgebras and Lie 2-superalgebras    [PDF]

Tao Zhang, Zhangju Liu

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.

View original: http://arxiv.org/abs/1301.2839