拟Hopf代数上BHQ何时是预辫子monoidal范畴

设H为带有可逆对极的拟Hopf代数, B为左拟Yetter-Drinfeld模代数,并且^H_BQ为拟Hopf Yetter-Drinfeld(H,B)-模范畴。讨论了范畴^H_BQ何时是预辫子monoidal范畴。假设B是H交换的,则拟Hopf Yetter-Drinfeld模范畴^HQ上的辫子诱导出^H_BQ上的预辫子当且仅当^H_BQ中的每一个对象是dyslectic。

When is BHQ a pre-braided category over quasi-Hopf algebras

Let H be a quasi-Hopf algebra with invertible antipode, B a left quasi Yetter-Drinfeld module algebra and ^H_BQ the category of quasi Hopf Yetter-Drinfeld (H,B)-modules. It is discussed when the category ^H_BQ is a pre-braided monoidal category. The following is proved: assume that B is H-commutative, then the braiding on the category of quasi Yetter-Drinfeld modules HQ induces a pre-braiding on ^H_BQ if and only if every object of H_BQ is dyslectic.