Amenable discrete quantum groups

Structural Properties of Inner Amenable Discrete Groups

structural properties of inner amenable discrete groups

Amenable Actions and Exactness for Discrete Groups

It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...

Amenable Groups

Throughout we let Γ be a discrete group. For f : Γ → C and each s ∈ Γ we define the left translation action by (s.f)(t) = f(s−1t). Definition 1.1. A group Γ is amenable is there exists a state μ on l∞(Γ) which is invariant under the left translation action: for all s ∈ Γ and f ∈ l∞(Γ), μ(s.f) = μ(f). Example 1.2. Finite groups are amenable: take the state which sends χ{s} to 1 |Γ| for each s ∈ ...

Recurrent Points and Discrete Points for Elementary Amenable Groups

Let fig be the Stone-Cech compactification of a group G, Aa the set of all almost periodic points in G, Ka c[U { supp eLIM(G)}] and Ra the set of all recurrent points in fiG. In this paper we will study the relationships between Ka and Ra, and between Aa and Ra. We will show that for any infinite elementary amenable group G, Aa Ra and RaKa =/= .