Universal coacting Hopf algebra of a finite dimensional Lie-Yamaguti algebra

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-10-03 DOI:10.1016/j.laa.2024.09.017

Saikat Goswami , Satyendra Kumar Mishra , Goutam Mukherjee

引用次数: 0

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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有限维李-山古提代数的普适共作用霍普夫代数

M.E. Sweedler 首次构造了一个代数的普遍霍普夫代数。众所周知，现有概念的对偶概念在霍普夫代数理论中起着主导作用。尤.马宁（Yu. I. Manin）和丹巴拉（D. Tambara）在不同的著作中介绍了斯韦德勒构造的对偶概念。在本文中，我们为有限维李-山古提代数构造了一个普代数。我们证明了这个普代数具有双代数结构，从而为有限维李-山口组代数建立了一个普协合霍普夫代数。此外，我们还开发了我们结果的表示理论版本。作为应用，我们描述了有限维李-山口组代数的自变群特征，并对其所有无性群分级进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.