Abstract
Introduction. Suppose that A is a semisimple Hopf algebra over a field of characteristic 0, or that A is a semisimple cosemisimple involutory Hopf algebra over a field k of characteristic p > dim A. In this paper we prove that the group AutHopf(A) of Hopf algebra automorphisms of A is finite. We show that the semigroup EndHOpf(A) of Hopf algebra endomorphisms of A is also finite as a corollary. Generally the group of Hopf algebra automorphisms of a finite-dimensional Hopf algebra need not be finite. For any positive integer n and any field k, we construct a family of finite-dimensional Hopf algebras over k with automorphism group GLn(k). The fact that AutHopf(A) is finite is a consequence of a theorem of
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