New Turaev Braided Group Categories and Group Corings Based on Quasi-Hopf Group Coalgebras

摘要

In this article, we first study the pre-T-category over a group π for a family of algebras {A_α}_α∈_π and naturally introduce the notion of a quasi-Hopf π-coalgebra. Then we prove that the category of representations of quasitriangular quasi-Hopf π-coalgebras is exactly a Turaev braided π-category in the sense of Turaev. As a dual case, we also investigate the notion of a coquasitriangular coquasi-Hopf π-algebras and show that the category of corepresentations of coquasitriangular coquasi-Hopf π-algebras is also a Turaev braided π-category. Finally, we study the π-coring C{black-letter} and the π-Doi-Hopf module for quasi-Hopf π-coalgebras, and show that the category of right-right π-Doi-Hopf modules □(H)_□ ~(π-C) is isomorphic to the category of right C{black-letter} - π-comodules □~(π-C){black-letter}.