Related papers: Classifiability of crossed products by nonamenable…
It was shown by Rordam and the second named author that a countable group G admits an action on a compact space such that the crossed product is a Kirchberg algebra if, and only if, G is exact and non-amenable. This construction allows a…
We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits continuously many amenable minimal Cantor…
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg…
We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are simple, separable, unital, nuclear and satisfy the UCT: these…
We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a…
We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact semi-simple Lie groups, but excludes all inner…
We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed products of minimal such actions are…
I combine recent results in the structure theory of nuclear C*-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group C*-algebras…
We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. We…
When a locally compact group acts on a C*-correspondence, it also acts on the associated Cuntz-Pimsner algebra in a natural way. Hao and Ng have shown that when the group is amenable the Cuntz-Pimsner algebra of the crossed product…
Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra…
Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterisation of…
We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…
We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…
The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some usefull properties of subgroups and amalgamated…
We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…
By employing the external Kasparov product, Hawkins, Skalski, White and Zacharias constructed spectral triples on crossed product C$^\ast$-algebras by equicontinuous actions of discrete groups. They further raised the question for whether…
We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C$^*$-algebras, as a weakening of amenability where all the relevant approximations are done in the uniform trace norm. We characterize tracial…
In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…
We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…