An Equivariant Brauer Group and Actions of Groups on C*-algebras
| dc.creator | Crocker, David | |
| dc.creator | Kumjian, Alex | |
| dc.creator | Raeburn, Iain | |
| dc.creator | Williams, Dana | |
| dc.date | 1994-12-12 | |
| dc.date.accessioned | 2026-07-07T09:13:31Z | |
| dc.date.available | 2026-07-07T09:13:31Z | |
| dc.description | Suppose that $(G,T)$ is a second countable locally compact transformation group given by a homomorphism $\ell:G\to\Homeo(T)$, and that $A$ is a separable continuous-trace \cs-algebra with spectrum $T$. An action $α:G\to\Aut(A)$ 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: $[A,α][B,β] = [A\Ttensor B,α\tensorβ]$, 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 http://coos.dartmouth.edu/~dana/dana.html | |
| dc.description | 28 pages, AMS-LaTeX v1.1 | |
| dc.identifier | https://arxiv.org/abs/funct-an/9412002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9412002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152352 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | An Equivariant Brauer Group and Actions of Groups on C*-algebras | |
| dc.type | text |