Doi-Koppinen modules for quantum groupoids

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.Comment: 14 pages, LaTeX; final version to appear in J. Pure Appl. Algebr

Two elementary proofs of Katsaras’ Theorem on padic compactoids

Contains fulltext : 40______(1).pdf (publisher's version ) (Open Access

A note on Taylor's Brauer group

We make clear that some of the properties of central separable algebras without unit, as announced by Taylor and Raeburn, are only valid under the assumption that the algebra in question is flat. This leads to the introduction of two possibly different versions of the big Brauer group. Both of them inject into the second étale cohomology group, and one of them is isomorphic to it.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Brauer Groups and the Cohomology of Graded Rings

X, 261 tr.; 23 cm