AN EQUIVARIANT BRAUER GROUP AND ACTIONS OF GROUPS ON C-ASTERISK-ALGEBRAS

Suppose that (G, T) is a second countable locally compact transformati on group given by a homomorphism l: G --> Homeo(T), and that A is a se parable continuous-trace C-algebra with spectrum T. An action alpha: G --> Aut(A) is said to cover l if the induced action of G on T coinci des with the original one. We prove that the set Br,(T) of Morita equi valence classes of such systems forms a group with multiplication give n by the balanced tensor product: [A, alpha][B, beta] = [A x C-0(T), B , alpha x beta], and we refer to Br-G(T) as the Equivariant Brauer Gro up. We give a detailed analysis of the structure of Br-G(T) in terms o f the Moore cohomology of the group G and the integral cohomology of t he space T. Using this, we can characterize the stable continuous-trac e C-algebras with spectrum T which admit actions covering l. In parti cular, we prove that if G = R, then every stable continuous-trace C-a lgebra admits an (essentially unique) action covering l, thereby subst antially improving results of Raeburn and Rosenberg. (C) 1997 Academic Press.