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Algebras graded by discrete Doi-Hopf data and the Drinfeld double of a Hopf group-coalgebra
Journal Contribution - Journal Article
We study Doi-Hopf data and Doi-Hopf modules for Hopf group-coalgebras. We introduce modules graded by a discrete Doi-Hopf datum; to a Doi-Hopf datum over a Hopf group coalgebra, we associate an algebra graded by the underlying discrete Doi-Hopf datum, using a smash product type construction. The category of Doi-Hopf modules is then isomorphic to the category of graded modules over this algebra. This is applied to the category of Yetter-Drinfeld modules over a Hopf group coalgebra, leading to the construction of the Drinfeld double. It is shown that this Drinfeld double is a quasitriangular $\GG$-graded Hopf algebra.
Journal: Algebras and Representation Theory
ISSN: 1386-923X
Volume: 16
Pages: 155-192
Publication year:2013
Keywords:Hopf group-coalgebra, duality, Doi-Hopf module, Yetter-Drinfeld module