Classification of Finite-dimensional Basic Hopf Algebras According to Their Representation Type

The main aim of this paper is to give the classification of finite-dimensional basic Hopf algebras according to their representation type. We attach every finite-dimensional basic Hopf algebra H a natural number n(H), which will help us to determine the representation type of H. The class of finite-dimensional basic Hopf algebras of finite representation type is determined completely. A complete list of local Frobenius algebras of tame type is given. By using this list, we get all possible algebraic structures of tame basic Hopf algebras.