Metric aspects of noncommutative homogeneous spaces

Details Metric aspects of noncommutative homogeneous spaces Metric aspects of noncommutative homogeneous spaces

2008-10-26

arxiv.org/abs/0810.4694v2

J. Funct. Anal. 257 (2009), no. 7, 2325--2350

Mathematics

Operator Algebras

Minor change

Scientific paper

For a closed cocompact subgroup $\Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $\rho:\hat{K}\to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations $C^*(\hat{G}/\Gamma, \rho)$ of the homogeneous space $G/\Gamma$, generalizing Rieffel's construction of quantum Heisenberg manifolds. We show that when $G$ is a Lie group and $G/\Gamma$ is connected, given any norm on the Lie algebra of $G$, the seminorm on $C^*(\hat{G}/\Gamma, \rho)$ induced by the derivation map of the canonical $G$-action defines a compact quantum metric. Furthermore, it is shown that this compact quantum metric space depends on $\rho$ continuously, with respect to quantum Gromov-Hausdorff distances.

Affiliated with

Also associated with

No associations

Rating

Metric aspects of noncommutative homogeneous spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Metric aspects of noncommutative homogeneous spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metric aspects of noncommutative homogeneous spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-595281