کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4616485 | 1339351 | 2013 | 12 صفحه PDF | دانلود رایگان |
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 L1L1-algebra of locally compact quantum groups. In particular, we obtain a criterion that distinguishes discreteness from the Radon–Nikodym property in this setting.
Journal: Journal of Mathematical Analysis and Applications - Volume 406, Issue 1, 1 October 2013, Pages 22–33