We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

Let A be a unital simple direct limit of recursive subhomogeneous algebras with no dimension growth. We give criteria which specify exactly when A has real rank zero, and exactly when A has the Property (SP): every nonzero hereditary subalgebra of A contains a nonzero projection. Specifically, A has real rank zero if and only if the image of K0(A) in Aff(T (A)) is dense, and A has the Property ...

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups. Throughout this paper N will denote a finite von Neumann algebra with a fixed normal faithful tracial state τ .

We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many L ∞-eigenvalues. We make use of some analogs of basic results from the theory of finite-rank modules associated to an extension of measure-preserving systems in the setting of a non-singular base.

We continue the study of Rokhlin entropy, an isomorphism invariant for p.m.p. actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite generator theorem and use it to establish subadditivity and semi-continuity properties of Rokhlin entropy. We also obtain formulas for Rokhlin entropy in terms of ergodic decompositions and inverse limits. Finally, we clarify...

A countable group Γ is called shift-minimal if every non-trivial measure preserving action of Γ weakly contained in the Bernoulli shift Γ y ([0, 1] , λ ) is free. We show that any group Γ whose reduced C∗-algebra Cr(Γ) admits a unique tracial state is shift-minimal, and that any group Γ admitting a free measure preserving action of cost> 1 contains a finite normal subgroup N such that Γ/N is sh...