Doi-Koppinen modules for quantum groupoids

Details Doi-Koppinen modules for quantum groupoids Doi-Koppinen modules for quantum groupoids

2001-01-08

arxiv.org/abs/math/0101064v2

Mathematics

Quantum Algebra

14 pages, LaTeX; final version to appear in J. Pure Appl. Algebra

Scientific paper

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.

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