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

Pub Date : 2024-08-21 DOI:10.1007/s10468-024-10284-8

Jing Yu, Kangqiao Li, Gongxiang Liu

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引用次数: 0

摘要

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。

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Hopf Algebras with the Dual Chevalley Property of Finite Corepresentation Type

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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