Related papers: Actions on classifiable C*-algebras without equiva…

We show that the Liouville property and Reiter's condition are equivalent for semigroupoids. This result applies to semigroups as well as semigroup actions. In the special case of measured groupoids and locally compact groupoids, our result…

We give a sufficient condition for a countable group $G$ to possess a probability measure $\mu$ that admits a non-trivial $\mu$-boundary modeled in the space $\mathrm{Sub}_{\mathrm{am}}(G)$ of amenable subgroups of $G$. In particular, for…

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

We study the link between stably finiteness and stably projectionless-ness for $C^*$-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by $4$; otherwise, they…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

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 investigate the notions of amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say $UP(I,A)$, where $A$ is a Banach algebra equipped with a non-zero character. We show that…

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any…

A trace on a C*-algebra is amenable (resp. quasidiagonal) if it admits a net of completely positive, contractive maps into matrix algebras which approximately preserve the trace and are approximately multiplicative in the 2-norm (resp.…

An example is given of a simple, unital C*-algebra which contains an infinite and a non-zero finite projection. This C*-algebra is also an example of an infinite simple C*-algebra which is not purely infinite. A corner of this C*-algebra is…

We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear C*-algebras with stabilised property Gamma and $\mathrm{Cu}(A) \cong…

We study the group $C^*$-algebras $C^*_{L^{p+}}(G)$ - constructed from $L^p$-integrability properties of matrix coefficients of unitary representations - of locally compact groups $G$ acting on (semi-)homogeneous trees of sufficiently large…

We give the first examples of \'etale (non-Hausdorff) groupoids $\mathcal G$ whose $C^*$-algebras contain singular elements that cannot be approximated by singular elements in $\mathcal C_c(\mathcal G)$. We provide two examples: one is a…

Singular actions on C*-algebras are automorphic group actions on C*-algebras, where the group need not be locally compact, or the action need not be strongly continuous. We study the covariant representation theory of such actions. In the…

We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…

We prove that, if a discrete group $G$ is not inner amenable, then the unit group of the ring of operators affiliated with the group von Neumann algebra of $G$ is non-amenable with respect to the topology generated by its rank metric. This…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

We investigate when discrete, amenable groups have $C^*$-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then…

In this paper we will introduce the tracial Rokhlin property for an inclusion of separable simple unital C*-algebras $P \subset A$ with finite index in the sense of Watatani, and prove theorems of the following type. Suppose that $A$…