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• W2953188839 abstract "Suppose that $(G,T)$ is a second countable locally compact transformation group given by a homomorphism $ell:GtoHomeo(T)$, and that $A$ is a separable continuous-trace cs-algebra with spectrum $T$. An action $alpha:GtoAut(A)$ is said to cover $ell$ if the induced action of $G$ on $T$ coincides with the original one. We prove that the set $brgt$ of Morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product: $[A,alpha][B,beta] = [ATtensor B,alphatensorbeta]$, and we refer to $brgt$ as the Equivariant Brauer Group. We give a detailed analysis of the structure of $brgt$ in terms of the Moore cohomology of the group $G$ and the integral cohomology of the space $T$. Using this, we can characterize the stable continuous-trace cs-algebras with spectrum $T$ which admit actions covering $ell$. In particular, we prove that if $G=R$, then every stable continuous-trace cs-algebra admits an (essentially unique) action covering~$ell$, thereby substantially improving results of Raeburn and Rosenberg. Versions of this paper in *.dvi and *.ps form are available via World wide web servers at this http URL" @default.
• W2953188839 created "2019-06-27" @default.
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• W2953188839 date "1994-12-12" @default.
• W2953188839 modified "2023-09-27" @default.
• W2953188839 title "An Equivariant Brauer Group and Actions of Groups on C*-algebras" @default.
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• W2953188839 hasPublicationYear "1994" @default.
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