阿贝尔扩展上的最小三角形结构

Pub Date : 2024-01-12 DOI:10.1007/s10468-023-10250-w

Hong Fei Zhang, Kun Zhou

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引用次数: 0

摘要

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。

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Minimal Triangular Structures on Abelian Extensions

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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