Super 3-Lie Algebras Induced by Super Lie Algebras

TL;DR

This paper introduces super n-Lie algebras derived from super Lie algebras with supertrace, constructing a series of super 3-Lie algebras from Clifford algebra super Lie algebras using matrix representations.

Contribution

It defines super n-Lie algebras and constructs a new class of super 3-Lie algebras from Clifford algebra super Lie algebras with supertrace and spinor representations.

Findings

Constructed super 3-Lie algebras labeled by positive even integers.

Established a method to derive super n-Lie algebras from super Lie algebras.

Applied supertrace and matrix representations in the construction process.

Abstract

We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a Clifford algebra with even number of generators and making use of a matrix representation of this super Lie algebra given by a supermodule of spinors we construct a series of super 3-Lie algebras labeled by positive even integers.