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

2025/06/02 by Goswami, Saikat, Mishra, Satyendra Kumar, Mukherjee, Goutam · 1 citation
#16D90 #16T05 #16T10 #17A30 #17A36 #17A60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2506.01328

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.

Citations

• Deformation cohomology of morphisms of Lie-Yamaguti algebras
• On equivariant Lie-Yamaguti algebras and related structures
• The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary
• Deformations and extensions of Lie–Yamaguti algebras
• Irreducible Lie-Yamaguti algebras
• Irreducible Lie–Yamaguti algebras
• Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces
• Invariant Affine Connections on Homogeneous Spaces

Cited by

• Universal Coacting Hopf Algebra of a finite-dimensional Algebra over an Operad

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• Lie-Yamaguti Algebra Bundle