Title

Hopf algebras of prime dimension in positive characteristic

Document Type

Article

Publication Date

6-1-2019

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.

Publication Source (Journal or Book title)

Bulletin of the London Mathematical Society

First Page

459

Last Page

465

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