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arXiv · 2506.01328

Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra

Saikat Goswami·Satyendra Kumar Mishra·Goutam Mukherjee
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Abstract

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.

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Saikat Goswami, Satyendra Kumar Mishra, Goutam Mukherjee. 2025-06-02. Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra. https://doi.org/10.1016/j.laa.2024.09.017

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