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Proceedings of the American Mathematical Society
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
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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.


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Additional Information

S. Caenepeel
Affiliation: Faculty of Applied Sciences, Vrije Universiteit Brussel, VUB, B-1050 Brussels, Belgium
Email: scaenepe@vub.ac.be

F. Van Oystaeyen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Email: fred.vanoystaeyen@ua.ac.be

Y. H. Zhang
Affiliation: School of Mathematics and Computing Science, Victoria University of Wellington, Wellington, New Zealand
Email: yinhuo.zhang@vuw.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08041-X
PII: S 0002-9939(05)08041-X
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