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3-Lie Superalgebras Induced by Lie Superalgebras
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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.
Title: 3-Lie Superalgebras Induced by Lie Superalgebras
Description:
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.
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