3-Lie Superalgebras Induced by Lie Superalgebras

Axioms

Viktor Abramov¹ 

[1] Institute of Mathematics and Statistics, University of Tartu, 50409 Tartu, Estonia;

关键词: Lie superalgebra;    supertrace;    commutative superalgebra;    3-Lie superalgebra;   

DOI  :  10.3390/axioms8010021

来源: DOAJ

【 摘 要 】

We show that given a Lie superalgebra and an element of its dual space, one can construct the 3-Lie superalgebra. We apply this approach to Lie superalgebra of $(m,n)$ -block matrices taking a supertrace of a matrix as the element of dual space. Then we also apply this approach to commutative superalgebra and the Lie superalgebra of its derivations to construct 3-Lie superalgebra. The graded Lie brackets are constructed by means of a derivation and involution of commutative superalgebra, and we use them to construct 3-Lie superalgebras.

【 授权许可】

Unknown