A STRUCTURE THEOREM FOR QUASI-HOPF BIMODULE COALGEBRAS

作者：Bulacu Daniel^*

来源：Theory and Applications of Categories, 2017, 32: 1-30.

• monoidal equivalence
• (bi)comodule algebra
• bimodule coalgebra
• structure theorem

Let H be a quasi-Hopf algebra. We show that any H-bimodule coalgebra C for which there exists an H-bimodule coalgebra morphism v : C -> H is isomorphic to what we will call a smash product coalgebra. To this end, we use an explicit monoidal equivalence between the category of two-sided two-cosided Hopf modules over H and the category of left Yetter-Drinfeld modules over H. This categorical method allows also to reobtain the structure theorem for a quasi-Hopf (bi)comodule algebra given in [Panaite, Van Oystaeyen, 2007] and [Dello, Panaite, Van Oystaeyen, Zhang, 2016].

• 出版日期2017