Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras

Abstract

Let $T$ be a Lie-Yamaguti algebra such that its standard enveloping Lie algebra $L(T)$ is semisimple and $[T, T, T]=T$. Then we give a description of representations of $T$ in terms of representations of $L(T)$ with certain additional data. Similarly, if $(T, \sigma)$ is an infinitesimal $s$-manifold such that $L(T)$ is semisimple, then any representation of $(T, \sigma)$ comes from a representation of $L(T)$.