Simplicity in the Faulkner construction

Abstract

We revisit the Faulkner construction of metric 3-Leibniz algebras admitting an embedding Lie (super)algebra. In the case of positive-definite signature, we relate the various notions of simplicity: of the 3-algebra, of the representation and of the embedding Lie (super)algebra. This reduces their classification to the extant classifications of simple Lie (super)algebras.