Algebraic quantum hypergroups of discrete type

Abstract

In this paper we will study some structures of algebraic quantum hypergroups. First, we construct more examples of algebraic quantum hypergroups of discrete type. Next, we introduce the notion of a generalized quasi-Frobenius multiplier Hopf algebra and then show that generalized quasi-Frobenius multiplier Hopf algebras are a class of algebraic quantum hypergroups of discrete type. We also give some equivalent conditions for an algebraic quantum group to be of discrete type. Finally, we study sub-algebraic quantum hypergroups of discrete type and quotients of algebraic quantum hypergroups of discrete type.