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arXiv · 1810.00476

Hopf algebras of prime dimension in positive characteristic

Siu-Hung Ng·Xingting Wang
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Abstract

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension $p$ over a field of characteristic $q>0$ is commutative and cocommutative when $q=2$ or $p<4q$. This problem remains open in positive characteristic when $2<q<p/4$.

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BibTeXRIS

Siu-Hung Ng, Xingting Wang. 2018-09-30. Hopf algebras of prime dimension in positive characteristic. https://doi.org/10.1112/blms.12242

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