Constructing New Crossed Group Categories Over Weak Hopf Group Algebras

Abstract

Let π be a group. The main purpose of this paper is to provide further examples of crossed π-categories in the sense of Turaev. For this, we first introduce the notion of weak Hopf π-algebra as the dual notion of weak Hopf π-coalgebra and investigate the properties of weak Hopf π-algebra keeping close to weak Hopf algebra in sense of Böhm et al. It is shown that the category of the copresentations of weak Hopf π-algebra is braided crossed π-category. Finally, we shall consider the notion of weak Doi-Hopf group module in the weak Hopf π-algebra setting, and discuss the separability of a class of functors for the category of weak Doi-Hopf π-modules to the category of comodule over a suitable coalgebras. Also, the applications of our theories are presented.

The Morita contexts and galois extensions for weak Hopf group coalgebras

“…Using the theory of Hopf group coalgebras, [13] generalized Morita contexts in the setting of group corings. Dually, the authors also investigated some properties of (weak)Hopf group algebras in [14][15].…”