The Haagerup property for locally compact quantum groups

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

The Haagerup property, Property (T) and the Baum-Connes conjecture for locally compact Kac-Moody groups

We indicate which symmetrizable locally compact affine or hyperbolic Kac-Moody groups satisfy Kazhdan’s Property (T), and those that satisfy its strong negation, the Haagerup property. This reveals a new class of hyperbolic Kac-Moody groups satisfying the Haagerup property, namely symmetrizable locally compact Kac-Moody groups of rank 2 or of rank 3 noncompact hyperbolic type. These groups thus...

Local Similarities and the Haagerup Property

A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that these groups have the Haagerup property (that is, they are a-T-menable in the sense of Gromov). The class includes Thompson’s groups, which have already been shown to have the Haagerup property by D. S. Farley, as well as many other groups acting...

Variants of a-T-menability for actions on non-commutative Lp-spaces

We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on Lp(M), the non-commutative Lp-space associated with the von Neumann algebra M. For a semi-finite von Neumann algebra M, we introduce a variant of property (H), namely property HLp(M), defined in terms of orthogonal representations o...

Representations of Multiplier Algebras in Spaces of Completely Bounded Maps

If G is a locally compact group, then the measure algebra M(G) and the completely bounded multipliers of the Fourier algebra McbA(G) can be seen to be dual objects to one another in a sense which generalises Pontryagin duality for abelian groups. We explore this duality in terms of representations of these algebras in spaces of completely bounded maps. This article is intended to give a tour of...