Mathematics – Operator Algebras
Scientific paper
2007-04-12
Mathematics
Operator Algebras
Mistake in the proof of Theorem 6.1 is corrected. To appear in Munster Journal of Mathematics. 42 pages
Scientific paper
We prove that a compact quantum group is coamenable if and only if its corepresentation ring is amenable. We further propose a Foelner condition for compact quantum groups and prove it to be equivalent to coamenability. Using this Foelner condition, we prove that for a coamenable compact quantum group with tracial Haar state, the enveloping von Neumann algebra is dimension flat over the Hopf algebra of matrix coefficients. This generalizes a theorem of Lueck from the group case to the quantum group case, and provides examples of compact quantum groups with vanishing L^2-Betti numbers.
No associations
LandOfFree
L^2-Betti numbers of coamenable quantum groups 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 L^2-Betti numbers of coamenable quantum groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and L^2-Betti numbers of coamenable quantum groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-148015