Hopf algebras of prime dimension in positive characteristic
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
Ng, S., & Wang, X. (2019). Hopf algebras of prime dimension in positive characteristic. Bulletin of the London Mathematical Society, 51 (3), 459-465. https://doi.org/10.1112/blms.12242