On the Exponent of Finite-Dimensional Non-Cosemisimple Hopf Algebras

2018/07/25 by Kangqiao Li, Li, Kangqiao, Shenglin Zhu +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1807.09450

openalex publication_date 2018/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1999, Y. Kashina introduced the exponent of a Hopf algebra. In this paper, we prove that the exponent of a finite dimensional non-cosemisimple Hopf algebra with Chevalley property in characteristic 0 is infinite, and the exponent of a finite dimensional non-cosemisimple pointed Hopf algebra in positive characteristic is finite.

Cited by

• A class of (infinite-dimensional) cosemisimple Hopf algebras constructed via abelian extensions

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