A note on representations of Lie-Yamaguti algebras induced by left Leibniz algebras

Fuente: arXiv
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Main Author: Issa, A. Nourou
Format: Preprint
Published: 2025
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author Issa, A. Nourou
author_facet Issa, A. Nourou
contents It is well-known that each left Leibniz algebra has a natural structure of a Lie-Yamaguti algebra. In this paper it is shown that every left representation of a left Leibniz algebra $(\mathfrak{g}, \cdot)$ induces naturally a representation of the Lie-Yamaguti algebra $(\mathfrak{g}, [,], [\![ , , ]\!])$ that is associated with $(\mathfrak{g}, \cdot)$. Moreover, it is proved that equivalent representations of $(\mathfrak{g}, \cdot)$ give equivalent representations of $(\mathfrak{g}, [,], [\![ , , ]\!])$.
format Preprint
id arxiv_https___arxiv_org_abs_2501_16163
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A note on representations of Lie-Yamaguti algebras induced by left Leibniz algebras
Issa, A. Nourou
Rings and Algebras
Representation Theory
It is well-known that each left Leibniz algebra has a natural structure of a Lie-Yamaguti algebra. In this paper it is shown that every left representation of a left Leibniz algebra $(\mathfrak{g}, \cdot)$ induces naturally a representation of the Lie-Yamaguti algebra $(\mathfrak{g}, [,], [\![ , , ]\!])$ that is associated with $(\mathfrak{g}, \cdot)$. Moreover, it is proved that equivalent representations of $(\mathfrak{g}, \cdot)$ give equivalent representations of $(\mathfrak{g}, [,], [\![ , , ]\!])$.
title A note on representations of Lie-Yamaguti algebras induced by left Leibniz algebras
topic Rings and Algebras
Representation Theory
url https://arxiv.org/abs/2501.16163