Omni-Lie Superalgebras and Lie 2-superalgebras
Rings and Algebras
2013-01-15 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1301.2839,
title = {Omni-Lie Superalgebras and Lie 2-superalgebras},
author = {Tao Zhang and Zhangju Liu},
journal= {arXiv preprint arXiv:1301.2839},
year = {2013}
}
Comments
14pages