Hopf Algebras with the Dual Chevalley Property of Finite Corepresentation Type

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-08-21 DOI:10.1007/s10468-024-10284-8

Jing Yu, Kangqiao Li, Gongxiang Liu

引用次数: 0

Abstract

Let H be a finite-dimensional Hopf algebra over an algebraically closed field \(\Bbbk \) with the dual Chevalley property. We prove that H is of finite corepresentation type if and only if it is coNakayama, if and only if the link quiver \(\textrm{Q}(H)\) of H is a disjoint union of basic cycles, if and only if the link-indecomposable component \(H_{(1)}\) containing \(\Bbbk 1\) is a pointed Hopf algebra and the link quiver of \(H_{(1)}\) is a basic cycle.

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具有有限核心呈现类型双重切瓦利性质的霍普夫代数方程

设 H 是代数闭域 \(\Bbbk \)上的有限维霍普夫代数，具有对偶切瓦利性质。我们证明，当且仅当 H 是 coNakayama 时，当且仅当 H 的 link quiver （\textrm{Q}(H)\）是基本循环的不相交联盟时，当且仅当包含 \(\Bbbk 1\) 的 link-indecomposable 组件 \(H_{(1)}\) 是尖的 Hopf 代数且 \(H_{(1)}\ 的 link quiver 是基本循环时，H 才是有限核呈现类型。

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.