INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES

Extensions of amenable groups by recurrent groupoids

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk’s group, Basilica group, groups associated with...

Structural Properties of Inner Amenable Discrete Groups

structural properties of inner amenable discrete groups

Invariant Means and the Structure of Inner Amenable Groups

We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first `-Betti number of G with that of the stabilizer subgroups. An analogous relationship is also shown to ...

Measured Quantum Groupoids with a Central Basis

In ([L2]), Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In an annex of [E6], Lesieur’s axioms have been simplified. In this article, we suppose that the basis is central; in that case, we prove that a specific sub-C∗ algebra is, in a sense, invariant under all the data which define the measured quantum group, which allow us to prov...