Duality, Cohomology, and Geometry of Locally Compact Quantum Groups

Details Duality, Cohomology, and Geometry of Locally Compact Quantum Groups Duality, Cohomology, and Geometry of Locally Compact Quantum Groups

2011-10-22

arxiv.org/abs/1110.4933v1

Mathematics

Functional Analysis

17 Pages

Scientific paper

In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally compact quantum group with two products which are operator versions of convolution and pointwise multiplication, respectively; we investigate the relation between these two products, and derive a formula linking them. Furthermore, we define some canonical module structures on these convolution algebras, and prove that certain topological properties of a quantum group, can be completely characterized in terms of cohomological properties of these modules. We also prove a quantum group version of a theorem of Hulanicki characterizing group amenability. Finally, we study the Radon--Nikodym property of the $L^1$-algebra of locally compact quantum groups. In particular, we obtain a criterion that distinguishes discreteness from the Radon--Nikodym property in this setting.

Affiliated with

Also associated with

No associations

Rating

Duality, Cohomology, and Geometry of Locally Compact 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 Duality, Cohomology, and Geometry of Locally Compact Quantum Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Duality, Cohomology, and Geometry of Locally Compact Quantum Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-564234