A note on representations of Lie-Yamaguti algebras induced by left Leibniz algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929688112267264 |
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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 |
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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 |