Super cocommutative Hopf algebras of finite representation type

Given an algebraically closed field k of characteristic p>5, we classify the finite algebraic k-supergroups whose algebras of measures are of finite representation type. Let G be such a supergroup and the largest ordinary algebraic k-group determined by G. We show that both and u(Lie(G)), the restricted enveloping algebra of Lie superalgebra of G, are of finite representation type. Moreover, only some special representation-finite algebraic k-groups of dimension zero are shown to appear if . The structure of G is almost determined by and u(Lie(G)). The Auslander–Reiten quivers are determined by showing that they are Nakayama algebras.