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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