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Doi-Koppinen modules for quantum groupoids

par Brzezinski, Tomasz ;Caenepeel, Stefaan;Militaru, Gigel
Référence Journal of pure and applied algebra, 175, 1-3, page (45-62)
Publication Publié, 2002-11

Article révisé par les pairs

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Résumé :

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 Böhm (Comm. Algebra 28 (2000) 4687) 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 properties of corresponding functors in the category of comodules of a coring. © 2002 Elsevier Science B.V. All rights reserved.