Eduardo Scarparo

activity

20152026

most citedHomology of odometers

13 citations · 44 across the 14 of their papers we have counts for

collaborators

16 papers

math.OA2026

Invariant measures and traces on groupoid $C^{*}$ -algebras

Alistair Miller, Eduardo Scarparo

We provide sufficient conditions for the existence of a trace on the essential $C^{*}$ -algebra of a (not necessarily Hausdorff) étale groupoid $G$ which extends an invari…

math.OA2024

Maximal ideals of reduced group C*-algebras and Thompson's groups

Kevin Aguyar Brix, Chris Bruce, Kang Li +1

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, for…

math.OA2023★ 1 cited

A tracial characterization of Furstenberg's $\times p, \times q$ conjecture

Chris Bruce, Eduardo Scarparo

We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers $p$ and $q$ , we show that Fursten…

math.OA2022

$C^{*}$ -irreducibility of commensurated subgroups

Kang Li, Eduardo Scarparo

Given a commensurated subgroup $Λ$ of a group $Γ$ , we completely characterize when the inclusion $Λ \leq Γ$ is $C^{*}$ -irreducible and provide new examples of such inclusions. In part…

math.GR2022

The AH conjecture for Cantor minimal dihedral systems

Eduardo Scarparo

The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal…

math.GR2021

A dichotomy for topological full groups

Eduardo Scarparo

Given a minimal action $α$ of a countable group on the Cantor set, we show that the alternating full group $A (α)$ is non-amenable if and only if the topological full group…

math.GR2021

Relatively amenable actions of Thompson's groups

Eduardo Scarparo

We investigate the notion of relatively amenable topological action and show that the action of Thompson's group $T$ on $S^{1}$ is relatively amenable with respect to Thompson's grou…

math.OA2021

Boundary maps and covariant representations

Mehrdad Kalantar, Eduardo Scarparo

We extend applications of Furstenberg boundary theory to the study of $C^{*}$ -algebras associated to minimal actions $Γ ↷ X$ of discrete groups $Γ$ on locally compa…

math.OA2020

Boundary maps, germs and quasi-regular representations

Mehrdad Kalantar, Eduardo Scarparo

We investigate the tracial and ideal structures of $C^{*}$ -algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps,…

math.OA2020

Almost finiteness and homology of certain non-free actions

Eduard Ortega, Eduardo Scarparo

We show that Cantor minimal $Z ⋊ Z_{2}$ -systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal…

math.OA2020★ 5 cited

A torsion-free algebraically C*-unique group

Eduardo Scarparo

Let $p$ and $q$ be multiplicatively independent integers. We show that the complex group ring of $Z [\frac{1}{pq}] ⋊ Z^{2}$ admits a unique $C^{*}$ -norm.…

math.OA2018★ 13 cited

Homology of odometers

Eduardo Scarparo

We compute the homology groups of transformation groupoids associated with odometers and show that certain infinite dihedral group odometers give rise to counterexamples to the HK…

math.OA2018★ 8 cited

$C^{*}$ -simplicity and representations of topological full groups of groupoids

Kevin Aguyar Brix, Eduardo Scarparo

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 par…

math.OA2017★ 3 cited

On the $C^{*}$ -algebra generated by the Koopman representation of a topological full group

Eduardo Scarparo

Let $(X, T, μ)$ be a Cantor minimal sytem and $[[T]]$ the associated topological full group. We analyze $C_{π}^{*} ([[T]])$ , where $π$ is the Koopman representation attached to the action…

math.GR2016★ 9 cited

Characterizations of locally finite actions of groups on sets

Eduardo Scarparo

We show that an action of a group on a set $X$ is locally finite if and only if $X$ is not equidecomposable with a proper subset of itself. As a consequence, a group is locally fin…

math.OA2015★ 5 cited

Supramenable groups and partial actions

Eduardo P. Scarparo

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 parti…

Invariant measures and traces on groupoid C∗-algebras

Maximal ideals of reduced group C*-algebras and Thompson's groups

A tracial characterization of Furstenberg's ×p,×q conjecture

C∗-irreducibility of commensurated subgroups

The AH conjecture for Cantor minimal dihedral systems

A dichotomy for topological full groups

Relatively amenable actions of Thompson's groups

Boundary maps and covariant representations

Boundary maps, germs and quasi-regular representations

Almost finiteness and homology of certain non-free actions

A torsion-free algebraically C*-unique group

Homology of odometers

C∗-simplicity and representations of topological full groups of groupoids

On the C∗-algebra generated by the Koopman representation of a topological full group

Characterizations of locally finite actions of groups on sets

Supramenable groups and partial actions

Invariant measures and traces on groupoid $C^{*}$ -algebras

A tracial characterization of Furstenberg's $\times p, \times q$ conjecture

$C^{*}$ -irreducibility of commensurated subgroups

$C^{*}$ -simplicity and representations of topological full groups of groupoids

On the $C^{*}$ -algebra generated by the Koopman representation of a topological full group