Locally Compact Quantum Groups. A von Neumann Algebra Approach

Locally Compact Quantum Groups. A von Neumann Algebra Approach

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68–92] locally ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

reiter’s properties for the actions of locally compact quantum goups on von neumann algebras

Reiter’s Properties for the Actions of Locally Compact Quantum Groups on Von Neumann Algebras

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter’s conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented.

Homological Algebra with Locally Compact Abelian Groups

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a...