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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.
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.
Keywords
Lie superalgebra; supertrace; commutative superalgebra; 3-Lie superalgebra
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: 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.
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