2011/10/22 by Mehrdad Kalantar, Kalantar, Mehrdad, Matthias Neufang +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #math.FA
paper · pdf · doi:10.48550/arxiv.1110.4933
17 Pages
arxiv created 2011/10/22 · openalex publication_date 2011/10/22 · arxiv updated 2011/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.