Related papers: $C^*$-uniqueness Results for Groupoids

We generalize the ideal completions of countable discrete groups, as introduced by Brown and Guentner, to second countable Hausdorff \'etale groupoids. Specifically, to every pair consisting of an algebraic ideal in the algebra of bounded…

Motivated by the problem of characterizing KMS states on the reduced C$^*$-algebras of \'etale groupoids, we show that the reduced norm on these algebras induces a C$^*$-norm on the group algebras of the isotropy groups. This C$^*$-norm…

We describe a construction by G\'abor Elek, associating C*-algebras with uniformly recurrent subgroups, in the language of groupoid C*-algebras. This allows us to simplify several proofs in the original paper and fully characterise their…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

We consider a locally compact Hausdorff groupoid $G$, and twist by a more general locally compact Hausdorff abelian group $\Gamma$ rather than the complex unit circle $\mathbb{T}$. We investigate the construction of $C^*$-algebras in…

This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\omega = \{\omega_t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G}$ induces an isomorphism of…

Let G be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem of Clark about groupoids whose $C^*$-algebras are CCR. We show that if the groupoid C*-algebra…

Given two locally compact Hausdorff groupoids $G$ and $H$ and a $(G,H)$-equivalence $Z$, one can construct the associated linking groupoid $L$. This is reminiscent of the linking algebra for Morita equivalent $C^*$-algebras. Indeed, Sims…

Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show that the image of this representation…

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…

Let G be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for G, which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which…

Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^*$-algebras. We show that if the groupoid $C^*$-algebra of $G$…

This paper continues our investigation into the question of when a homotopy $\omega = \{\omega_t\}_{t \in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of…

We show that a (not necessarily Hausdorff) etale, second countable groupoid G with totally disconnected unit space may be reconstructed solely from the algebraic structure of its ample semigroup S. We also show that C*(G) possesses a…

In this paper, we introduce properties including groupoid comparison, pure infiniteness and paradoxical comparison as well as a new algebraic tool called groupoid semigroup for locally compact Hausdorff \'{e}tale groupoids. We show these…

To every one-sided shift space $\mathsf{X}$ we associate a cover $\tilde{\mathsf{X}}$, a groupoid $\mathcal{G}_{\mathsf{X}}$ and a $\mathrm{C^*}$-algebra $\mathcal{O}_{\mathsf{X}}$. We characterize one-sided conjugacy, eventual conjugacy…

We show the singular ideal in a non-Hausdorff \'etale groupoid C*-algebra is zero if and only if every unit is contained, at the level of group representation theory, in the collection of subgroups of the unit's isotropy group obtained as…

Let $\Gamma$ be a discrete group. We show that if $\Gamma$ is nonamenable, then the algebraic tensor products $C^*_r(\Gamma)\otimes C^*_r(\Gamma)$ and $C^*(\Gamma)\otimes C^*_r(\Gamma)$ do not admit unique $C^*$-norms. Moreover, when…

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…

We prove that ideals in amenable second-countable non-Hausdorff \'etale groupoid $C^*$-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the…