Algebras Graded by Discrete Doi-Hopf Data and the Drinfeld Double of a Hopf Group-Coalgebra

作者：Bulacu Daniel; Caenepeel Stefaan^*

来源：Algebras and Representation Theory, 2013, 16(1): 155-192.

DOI：10.1007/s10468-011-9300-8

• Hopf group-coalgebra
• Duality
• Doi-Hopf module
• Yetter-Drinfeld module

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 -graded Hopf algebra.

• 出版日期2013-2