On the Structure of Twisted Group C ∗ -Algebras

Abstract

We first give general structural results for the twisted group algebras C*(G, σ) of a locally compact group G with large abelian subgroups. In particular, we use a theorem of Williams to realise C*(G, σ) as the sections of a C*-bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras. Next we use a device of Rosenberg to show that, when Γ is a discrete subgroup of a solvable Lie group G, the K-groups K * (C*(Γ, σ)) are isomorphic to certain twisted K-groups K*(G/Γ, δ(σ)) of the homogeneous space G/Γ, and we discuss how the twisting class δ(σ) ∈ H 3 (G/Γ, Z) depends on the cocycle σ