Representations of Lie-Yamaguti algebras with semisimple enveloping Lie algebras
Abstract
Let $T$ be a Lie-Yamaguti algebra whose 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 $L(T)$.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.16932
- arXiv:
- arXiv:2407.16932
- Bibcode:
- 2024arXiv240716932T
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory;
- Primary 17A30;
- Secondary 17A40;
- 17B60;
- 22F30