Minimal Triangular Structures on Abelian Extensions

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-01-12 DOI:10.1007/s10468-023-10250-w

Hong Fei Zhang, Kun Zhou

引用次数: 0

Abstract

We study minimal triangular structures on abelian extensions. In particular, we construct a family of minimal triangular semisimple Hopf algebras and prove that the Hopf algebra \(H_{b:y}\) in the semisimple Hopf algebras of dimension 16 classified by Y. Kashina in 2000 is minimal triangular Hopf algebra with smallest dimension among non-trivial semisimple triangular Hopf algebras (i.e. not group algebras or their dual).

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阿贝尔扩展上的最小三角形结构

摘要我们研究了无边扩展上的最小三角形结构。特别是，我们构建了一个最小三角形半简单霍普夫代数族，并证明卡希纳（Y. Kashina）在 2000 年分类的维数为 16 的半简单霍普夫代数中的霍普夫代数（Hopf algebra）是非三维半简单三角形霍普夫代数（即非群代数或其对偶）中维数最小的最小三角形霍普夫代数。

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

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.