Related papers: The Generalized Effros-Hahn Conjecture for Groupoi…

For a second-countable locally compact Hausdorff \'etale groupoid $\mathcal{G}$ with a continuous $2$-cocycle $\sigma$ we find conditions that guarantee that $\ell^1 (\mathcal{G},\sigma)$ has a unique $C^*$-norm.

Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our…

Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$…

From a suitable groupoid G, we show how to construct an amenable principal groupoid whose C*-algebra is a Kirchberg algebra which is KK-equivalent to C*(G). Using this construction, we show by example that many UCT Kirchberg algebras can be…

It is proved that the reduced group C*-algebra C*_{red}(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G_1*G_2 where |G_1|>=2 and |G_2|>=3. This follows…

Let $G$ be a Hausdorff, \'etale groupoid that is minimal and topologically principal. We show that $C^*_r(G)$ is purely infinite simple if and only if all the nonzero positive elements of $C_0(G^0)$ are infinite in $C_r^*(G)$. If $G$ is a…

We show that $B(H)$ for an infinite dimensional Hilbert space $H$ cannot be realized as the reduced twisted $C^*$-algebra of any locally compact Hausdorff \'etale groupoid. The proof is based on the canonical conditional expectation…

Given a second-countable, locally compact group $G$, we consider amenable $G$-actions on separable, stable, nuclear $\mathrm{C}^\ast$-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz…

We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

Given a locally compact \'etale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this…

We characterise, in several complementary ways, \'etale groupoids with locally compact Hausdorff space of units whose essential groupoid C*-algebra has the ideal intersection property, assuming that the groupoid is topologically transitive…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…

We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan…

The complex algebra of an inverse semigroup with finitely many idempotents in each $\mathcal D$-class is stably finite by a result of Munn. This can be proved fairly easily using $C^*$-algebras for inverse semigroups satisfying this…

We develop a theory of graph C*-algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a countably infinite set of edges. We show that…

The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…

We show that, if A is a separable simple unital C*-algebra which absorbs the Jiang-Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on…

We consider the universal Grigorchuk 2-group, i.e., the group such that every Grigorchuk 2-group is a quotient. We show that this group has a nice universal representation in the group of all functions f:{0,1,2}^N --> Aut(T_2), where T_2 is…