Isoclinism in regular Hom-Lie Yamaguti algebras
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915423516098560 |
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| author | Asif, Sania Sadraoui, Mohamed Amin |
| author_facet | Asif, Sania Sadraoui, Mohamed Amin |
| contents | In this paper, we develop the theory of \emph{isoclinism} for regular Hom-Lie Yamaguti algebras, a class that unifies several generalizations of Lie algebras. Although isomorphism implies isoclinism by definition, the converse is not true in general. We introduce the notion of a \emph{factor set} and use it to analyze the structure of isoclinism families. Our main result establishes that for finite-dimensional regular Hom-Lie Yamaguti algebras of the same dimension, isoclinism implies isomorphism. This generalizes recent classification theorems for Lie-Yamaguti algebras and Hom-Lie superalgebras, highlighting a strong rigidity property in the finite-dimensional setting. The proof relies on the existence of stem algebras and a decomposition theorem within isoclin families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoclinism in regular Hom-Lie Yamaguti algebras Asif, Sania Sadraoui, Mohamed Amin Rings and Algebras 17B55, 17B99, 17B63, 17A30, 17B40 In this paper, we develop the theory of \emph{isoclinism} for regular Hom-Lie Yamaguti algebras, a class that unifies several generalizations of Lie algebras. Although isomorphism implies isoclinism by definition, the converse is not true in general. We introduce the notion of a \emph{factor set} and use it to analyze the structure of isoclinism families. Our main result establishes that for finite-dimensional regular Hom-Lie Yamaguti algebras of the same dimension, isoclinism implies isomorphism. This generalizes recent classification theorems for Lie-Yamaguti algebras and Hom-Lie superalgebras, highlighting a strong rigidity property in the finite-dimensional setting. The proof relies on the existence of stem algebras and a decomposition theorem within isoclin families. |
| title | Isoclinism in regular Hom-Lie Yamaguti algebras |
| topic | Rings and Algebras 17B55, 17B99, 17B63, 17A30, 17B40 |
| url | https://arxiv.org/abs/2508.01631 |