Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913870418804736 |
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| author | Goswami, Saikat Mishra, Satyendra Kumar Mukherjee, Goutam |
| author_facet | Goswami, Saikat Mishra, Satyendra Kumar Mukherjee, Goutam |
| contents | M. E. Sweedler first constructed a universal Hopf algebra of an algebra. It is known that the dual notions to the existing ones play a dominant role in Hopf algebra theory. Yu. I. Manin and D. Tambara introduced the dual notion of Sweedler's construction in separate works. In this paper, we construct a universal algebra for a finite-dimensional Lie-Yamaguti algebra. We demonstrate that this universal algebra possesses a bialgebra structure, leading to a universal coacting Hopf algebra for a finite-dimensional Lie-Yamaguti algebra. Additionally, we develop a representation-theoretic version of our results. As an application, we characterize the automorphism group and classify all abelian group gradings of a finite-dimensional Lie-Yamaguti algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_01328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra Goswami, Saikat Mishra, Satyendra Kumar Mukherjee, Goutam Rings and Algebras 16D90, 16T05, 16T10, 17A30, 17A36, 17A60 M. E. Sweedler first constructed a universal Hopf algebra of an algebra. It is known that the dual notions to the existing ones play a dominant role in Hopf algebra theory. Yu. I. Manin and D. Tambara introduced the dual notion of Sweedler's construction in separate works. In this paper, we construct a universal algebra for a finite-dimensional Lie-Yamaguti algebra. We demonstrate that this universal algebra possesses a bialgebra structure, leading to a universal coacting Hopf algebra for a finite-dimensional Lie-Yamaguti algebra. Additionally, we develop a representation-theoretic version of our results. As an application, we characterize the automorphism group and classify all abelian group gradings of a finite-dimensional Lie-Yamaguti algebra. |
| title | Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra |
| topic | Rings and Algebras 16D90, 16T05, 16T10, 17A30, 17A36, 17A60 |
| url | https://arxiv.org/abs/2506.01328 |