Duality, cohomology, and geometry of locally compact quantum groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:406

Article

Kalantar, Mehrdad¹  Neufang, Matthias^1,2 

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[2] Univ Lille 1 Sci & Technol, UFR Math, Lab Math Paul Painleve, UMR CNRS 8524, F-59655 Villeneuve Dascq, France

关键词: Locally compact quantum groups;    Convolution algebras;    Cohomology;    Amenability;   

DOI  :  10.1016/j.jmaa.2013.04.024

来源: Elsevier

【 摘 要 】

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 L1-algebra of locally compact quantum groups. In particular, we obtain a criterion that distinguishes discreteness from the Radon-Nikodym property in this setting. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free