The equivariant Brauer group and twisted transformation group C*-algebras

Twisted transformation group C*-algebras associated to locally compact dyna mical systems (X = Y/N, G) are studied, where G is abelian, N is a closed s ubgroup of G, and Y is a locally trivial principal G-bundle over Z = Y/G. A n explicit homomorphism between H-2(G, C(X, T)) and the equivariant Brauer group of Crocker, Kumjian, Raeburn and Williams, Br-N(Z), is constructed, a nd this homomorphism is used to give conditions under which a twisted trans formation group C*-algebra C-0(X) x(tau, omega) G will be strongly Morita e quivalent to another twisted transformation group C*-algebra C-0(Z) x(Id,om ega) N These results are applied to the study of twisted group C*-algebras C*(Gamma, mu) where Gamma is a finitely generated torsion free two-step nil potent group.