Traces on non-commutative homogeneous spaces
Abstract
Description
We study properties of C*-algebraic deformations of homogeneous spaces $G/Γ$ which are equivariant in the sense that they preserve the natural action of $G$ by left translation. The center is shown to be isomorphic to $C(G/G_ρ^0)$ for a certain subgroup $G_ρ^0$ of $G$, and there is a 1-1 correspondence between normalised traces and probability measures on $G/G_ρ^0$. This makes it possible to represent the deformed algebra as operators over $L^2(G/Γ)$. Applications to K-theory are also mentioned.
12 pages, an error in the first version has been corrected. To appear in J. Funct. Anal
12 pages, an error in the first version has been corrected. To appear in J. Funct. Anal