## Illinois Journal of Mathematics

### The equivariant brauer group and twisted transformation group $C^{\ast}$-algebras

Judith A. Packer

#### Abstract

Twisted transformation group $C^{\ast}$-algebras associated to locally compact dynamical systems $(X = Y/N,G)$ are studied, where $G$ is abelian, $N$ is a closed subgroup of $G$, and $Y$ is a locally trivial principal $G$-bundle over $Z = Y/G$. An explicit homomorphism between $H^{2}(G,C(X,\mathbb{T}))$ and the equivariant Brauer group of Crocker, Kumjian, Raeburn and Williams, $Br_{N}(Z)$, is constructed, and this homomorphism is used to give conditions under which a twisted transformation group $C^{\ast}$-algebra $C_{0}(X) \times_{\tau,\omega}G$ will be strongly Morita equivalent to another twisted transformation group $C^{\ast}$-algebra $C_{0}(Z) \times_{Id,\omega}N$. These results are applied to the study of twisted group $C^{\ast}$-algebras $C^{\ast}(\Gamma,\mu)$ where $\Gamma$ is a finitely generated torsion free two-step nilpotent group.

#### Article information

Source
Illinois J. Math., Volume 43, Issue 4 (1999), 707-732.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256060688

Digital Object Identifier
doi:10.1215/ijm/1256060688

Mathematical Reviews number (MathSciNet)
MR1712519

Zentralblatt MATH identifier
0958.46037

#### Citation

Packer, Judith A. The equivariant brauer group and twisted transformation group $C^{\ast}$-algebras. Illinois J. Math. 43 (1999), no. 4, 707--732. doi:10.1215/ijm/1256060688. https://projecteuclid.org/euclid.ijm/1256060688