Traces on non-commutative homogeneous spaces

Details Traces on non-commutative homogeneous spaces Traces on non-commutative homogeneous spaces

2001-04-05

arxiv.org/abs/math/0104067v2

Mathematics

Operator Algebras

12 pages, an error in the first version has been corrected. To appear in J. Funct. Anal

Scientific paper

We study properties of C*-algebraic deformations of homogeneous spaces $G/\Gamma$ 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 $C(G/G_\rho^0)$ for a certain subgroup $G_\rho^0$ of $G$, and there is a 1-1 correspondence between normalised traces and probability measures on $G/G_\rho^0$. This makes it possible to represent the deformed algebra as operators over $L^2(G/\Gamma)$. Applications to K-theory are also mentioned.

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