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.
"Equivariant group cohomology and Brauer group." Bull. Belg. Math. Soc. Simon Stevin 10 (3) 451 - 459, September 2003. https://doi.org/10.36045/bbms/1063372349