The equivariant Brauer group of a group

Caenepeel, S.; Van Oystaeyen, F.; Zhang, Y.

doi:10.1090/S0002-9939-05-08041-X

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
DOI: https://doi.org/10.1090/S0002-9939-05-08041-X
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 (finite or infinite) over a commutative ring 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

to the infinite case of

. 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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