Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 5: 1195 - 1210

DOI: https://doi.org/10.1007/s11464-014-0347-9

RESEARCH ARTICLE

Omni-Lie superalgebras and Lie 2-superalgebras

  • Tao ZHANG ,
  • Zhangju LIU
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  • Department of Mathematics and LMAM, Peking University, Beijing 100871, China

Received date: 04 Jan 2013

Accepted date: 22 Nov 2013

Published date: 26 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Lie 2-superalgebra; Leibniz superalgebra; Dirac structure

Cite this article

Tao ZHANG , Zhangju LIU . Omni-Lie superalgebras and Lie 2-superalgebras[J]. Frontiers of Mathematics in China, 2014 , 9(5) : 1195 -1210 . DOI: 10.1007/s11464-014-0347-9

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