Doi-Koppinen modules for quantum groupoids

Brzezinski, Tomasz; Caenepeel, Stefaan; Militaru, Gigel

Doi-Koppinen modules for quantum groupoids

Authors

Brzezinski, Tomasz

Caenepeel, Stefaan

Militaru, Gigel

Description

A definition of a Doi-Koppinen datum over a noncommutative algebra is proposed. The idea is to replace a bialgebra in a standard Doi-Koppinen datum with a bialgebroid. The corresponding category of Doi-Koppinen modules over a noncommutative algebra is introduced. A weak Doi-Koppinen datum and module of [G. Bohm. Comm. Algebra, 28:4687--4698, 2000] are shown to be examples of a Doi-Koppinen datum and module over an algebra. A coring associated to a Doi-Koppinen datum over an algebra is constructed and various properties of induction and forgetful functors for Doi-Koppinen modules over an algebra are deduced from the properies of corresponding functors in the category of comodules of a coring.
14 pages, LaTeX; final version to appear in J. Pure Appl. Algebra