English

Doi-Koppinen modules for quantum groupoids

Quantum Algebra 2007-05-23 v2 Rings and Algebras

Abstract

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.

Keywords

Cite

@article{arxiv.math/0101064,
  title  = {Doi-Koppinen modules for quantum groupoids},
  author = {Tomasz Brzezinski and Stefaan Caenepeel and Gigel Militaru},
  journal= {arXiv preprint arXiv:math/0101064},
  year   = {2007}
}

Comments

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