Hopf C*-Algebras And Their Representations

Abstract

In this paper, we study the finite dimensional unitary representations of Hopf C*-algebras. First of all, we study the characters of representations, and show the orthogonal relations for characters of finite dimensional irreducible representations and the matrix coefficients of finite dimensional irreducible representations, these are generalizations of the results about repersentations of compact groups; also, we consider the representation algebras of Hopf C*-algebras, and prove a Peter-Weyl type theorem for representation algebras. Finally, we pose some open problems on Hopf C*-algebra theory for possible future development.