In this paper we prove that, for any Galois finite field extension $F/K$ on which a
separated group of operators $\Gamma$ is acting, there is an isomorphism between the
group of equivariant isomorphism classes of finite dimensional central simple
$K$-algebras endowed with a $\Gamma$-action and containing $F$ as an equivariant strictly
maximal subfield and the second equivariant cohomology group of the Galois group of the
extension.
Publié le : 2003-09-14
Classification:
Group cohomology,
Brauer group,
Azumaya algebra,
Galois extension,
group of operators,
12G05,
16H05,
16K50,
20J06
@article{1063372349,
author = {Cegarra, A. M. and Garz\'on, A.R.},
title = {Equivariant group cohomology and Brauer group},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {10},
number = {1},
year = {2003},
pages = { 451-459},
language = {en},
url = {http://dml.mathdoc.fr/item/1063372349}
}
Cegarra, A. M.; Garzón, A.R. Equivariant group cohomology and Brauer group. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp. 451-459. http://gdmltest.u-ga.fr/item/1063372349/