A Class of Quasitriangular Hopf Group Coalgebras and Drinfel'd Double

Abstract

Let G be a group. In this paper we investigate the notion of a quasitriangular Hopf G-coalgebra. We construct a class of smash product Hopf G-coalgebras and present a framework for constructing a quasitriangular Hopf G-coalgebra. As an application, we study an analog of the Drinfel'd double for a crossed Hopf G-coalgebra of finite type.