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 (g) under bar the largest ordinary algebraic k-group determined by g. We show that both (g) under bar 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 g not equal (g) under bar. The structure of g is almost determined by (g) under bar and u(Lie(g)). The Auslander-Reiten quivers are determined by showing that they are Nakayama algebras. (C) 2012 Elsevier Inc. All rights reserved.