On Cocommutative Hopf Algebras of Finite Representation Type

Abstract

Let G be a finite algebraic group, defined over an algebraically closed field k of characteristic p>0. Such a group decomposes into a semidirect product G=G0×Gred with a constant group Gred and a normal infinitesimal subgroup G0. If the principal block B0(G) of the group algebra H(G) has finite representation type, then both constituents have the same property, with at least one of them being semisimple. We determine the structure of the infinitesimal constituent G0 up to the classification of V-uniserial groups.