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

Abstract

In this article , we prove that if B is a simple binary-Lie superalgebra whose even part is isomorphic to sl 2 (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 sl 2 (F) not completely reducible.