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Axioms 2019, 8(1), 21; https://doi.org/10.3390/axioms8010021

3-Lie Superalgebras Induced by Lie Superalgebras

Institute of Mathematics and Statistics, University of Tartu, 50409 Tartu, Estonia
Received: 21 November 2018 / Revised: 30 January 2019 / Accepted: 31 January 2019 / Published: 6 February 2019
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Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Abramov, V. 3-Lie Superalgebras Induced by Lie Superalgebras. Axioms 2019, 8, 21.

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