Geodesic
A structure theorem for quasi-Hopf bimodule coalgebras
Theory and applications of categories, Tome 32 (2017), pp. 1-30

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Let H be a quasi-Hopf algebra. We show that any H-bimodule coalgebra C for which there exists an H-bimodule coalgebra morphism n : 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 by Panaite and Van Oystaeyen, and by Dello et al.

Publié le :
Classification : 16W30, 18D10, 16S34
Keywords: monoidal equivalence, (bi)comodule algebra, bimodule coalgebra, structure theorem 
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     author = {Daniel Bulacu},
     title = {A structure theorem for {quasi-Hopf} bimodule coalgebras},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a0/}
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Daniel Bulacu. A structure theorem for quasi-Hopf bimodule coalgebras. Theory and applications of categories, Tome 32 (2017), pp. 1-30. http://geodesic.mathdoc.fr/item/TAC_2017_32_a0/