Omni-Lie Superalgebras and Lie 2-superalgebras
Tao Zhang, Zhangju Liu
TL;DR
This paper introduces omni-Lie superalgebras, extending Weinstein's omni-Lie algebra to superalgebras, establishing a correspondence between Dirac structures and Lie superalgebra structures, and providing new examples of Leibniz superalgebras and Lie 2-superalgebras.
Contribution
It defines omni-Lie superalgebras and demonstrates their role in connecting Dirac structures with Lie superalgebra structures, offering novel algebraic frameworks.
Findings
Established a one-to-one correspondence between Dirac structures and Lie superalgebra structures.
Provided new examples of Leibniz superalgebras.
Extended the concept of omni-Lie algebras to the superalgebra setting.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology