Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras
Nobuyoshi Takahashi

TL;DR
This paper characterizes the representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras, linking them to representations of the enveloping algebra with added structure, and extends this to infinitesimal s-manifolds.
Contribution
It provides a description of Lie-Yamaguti algebra representations in terms of their semisimple enveloping Lie algebras, including additional data, and extends to infinitesimal s-manifolds.
Findings
Representations of Lie-Yamaguti algebras are described via their semisimple enveloping Lie algebras.
Any representation of an infinitesimal s-manifold with semisimple enveloping algebra derives from a Lie algebra representation.
Abstract
Let be a Lie-Yamaguti algebra such that its standard enveloping Lie algebra is semisimple and . Then we give a description of representations of in terms of representations of with certain additional data. Similarly, if is an infinitesimal -manifold such that is semisimple, then any representation of comes from a representation of .
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