Preprint Article Version 1 This version is not peer-reviewed

3-Lie Superalgebras Induced by Lie Superalgebras

Version 1 : Received: 21 November 2018 / Approved: 23 November 2018 / Online: 23 November 2018 (10:57:17 CET)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Axioms 2019, 8, 21
DOI: 10.3390/axioms8010021

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 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.

Subject Areas

Lie superalgebra; supertrace; commutative superalgebra; 3-Lie superalgebra

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