The isomorphism of the Brauer group with a Galois cohomology group can be described as follows. The automorphism group of the algebra of "n" × "n" matrices is the projective linear group PGL("n"). Since all central simple algebras over "K" become isomorphic to the matrix algebra over a separable closure of "K", the set of isomorphism classes of central simple algebras of degree "n" over "K" can be identified with the Galois cohomology set "H"1("K", PGL("n")). The class of a central simple algebra in "H"2("K", Gm) is the image of its class in "H"1 under the boundary homomorphism