On Simple Completely Reducible Binary-Lie Superalgebras over sl₂(F)

Manuel Arenas^*

Departamento de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.

DOI: 10.4236/apm.2015.55030                

Abstract

In this article, we prove that if B is a simple binary-Lie superalgebra whose even part is isomorphic to sl₂(F)  and whose odd part is a completely reducible binary-Lie-module over the even part, then B is a Lie superalgebra. We introduce also a binary-Lie module over which is sl₂(F) not completely reducible.

Keywords

Binary-Lie, Super-Algebras

Conflicts of Interest

The authors declare no conflicts of interest.

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