Equivariant central simple graded algebras and the equivariant Brauer-Wall group

We consider central simple Z/2-graded algebras over a field K of characteristic ≠2 acted on by a group G via graded automorphisms. The equivariant Brauer-Wall group BW(K,G) is defined by means of an equivalence relation among these algebras. Its structure as an Abelian group is completely determined using the known structure of the Brauer-Wall group BW(K) due to C.T.C. Wall. It is also shown that there is a homomorphism W(K,G)→BW(K,G) where W(K,G) is the equivariant Witt group defined by A. Fröhlich and A.M. McEvett.