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3-Lie Superalgebras Induced by Lie Superalgebras

Institute of Mathematics and Statistics, University of Tartu, 50409 Tartu, Estonia
Axioms 2019, 8(1), 21; https://doi.org/10.3390/axioms8010021
Received: 21 November 2018 / Revised: 30 January 2019 / Accepted: 31 January 2019 / Published: 6 February 2019
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. View Full-Text
Keywords: Lie superalgebra; supertrace; commutative superalgebra; 3-Lie superalgebra Lie superalgebra; supertrace; commutative superalgebra; 3-Lie superalgebra
MDPI and ACS Style

Abramov, V. 3-Lie Superalgebras Induced by Lie Superalgebras. Axioms 2019, 8, 21.

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