Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The equivariant Brauer group of a group

Authors: S. Caenepeel, F. Van Oystaeyen and Y. H. Zhang
Journal: Proc. Amer. Math. Soc. 134 (2006), 959-972
MSC (2000): Primary 16H05, 16W50
Published electronically: August 16, 2005
MathSciNet review: 2196026
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Brauer group ${\operatorname{BM}'}(k,G)$ of a group $G$ (finite or infinite) over a commutative ring $k$ with identity. A split exact sequence

\begin{displaymath}1\longrightarrow \operatorname{Br}'(k)\longrightarrow \oper... ...}'(k,G)\longrightarrow\operatorname{Gal}(k,G) \longrightarrow 1\end{displaymath}

is obtained. This generalizes the Fröhlich-Wall exact sequence from the case of a field to the case of a commutative ring, and generalizes the Picco-Platzeck exact sequence from the finite case of $G$ to the infinite case of $G$. Here $\operatorname{Br}'(k)$ is the Brauer-Taylor group of Azumaya algebras (not necessarily with unit). The method developed in this paper might provide a key to computing the equivariant Brauer group of an infinite quantum group.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16H05, 16W50

Retrieve articles in all journals with MSC (2000): 16H05, 16W50

Additional Information

S. Caenepeel
Affiliation: Faculty of Applied Sciences, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium

F. Van Oystaeyen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium

Y. H. Zhang
Affiliation: School of Mathematics and Computing Science, Victoria University of Wellington, Wellington, New Zealand

Keywords: Equivariant Brauer group, Taylor Azumaya algebra
Received by editor(s): December 16, 2003
Received by editor(s) in revised form: August 16, 2004, and November 1, 2004
Published electronically: August 16, 2005
Additional Notes: The third named author was supported by the Marsden Fund
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society