Boundary maps, germs and quasi-regular representations

@article{Kalantar2022BoundaryMG,
title={Boundary maps, germs and quasi-regular representations},
year={2022}
}
• Published 6 October 2020
• Mathematics
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, namely $\Gamma$-equivariant unital completely positive maps from $\Gamma$-$C^*$-algebras to $C(\partial_F\Gamma)$, where $\partial_F\Gamma$ denotes the Furstenberg boundary of a group $\Gamma$. For a unitary representation $\pi$ coming from the groupoid of germs of a boundary action, we show that there is a unique…
4 Citations
A type I conjecture and boundary representations of hyperbolic groups
• Mathematics
• 2021
We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G associated with non-singular G-spaces. We deduce that any
Boundary maps and covariant representations
• Mathematics
• 2021
We extend applications of Furstenberg boundary theory to the study of C∗-algebras associated to minimal actions ΓyX of discrete groups Γ on locally compact spaces X. We introduce boundary maps on (Γ,
RELATIVELY AMENABLE ACTIONS OF THOMPSON’S GROUPS
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 group F. We
The ideal intersection property for essential groupoid C*-algebras
We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C∗-algebra has the ideal intersection property, assuming that

References

SHOWING 1-10 OF 69 REFERENCES
Furstenberg boundaries for pairs of groups
• N. Monod
• Mathematics
Ergodic Theory and Dynamical Systems
• 2021
Furstenberg has associated to every topological group $G$ a universal boundary $\unicode[STIX]{x2202}(G)$ . If we consider in addition a subgroup $H<G$ , the relative notion of $(G,H)$ -boundaries
The ideal intersection property for essential groupoid C*-algebras
We characterise, in several complementary ways, étale groupoids with locally compact Hausdorff space of units whose essential groupoid C∗-algebra has the ideal intersection property, assuming that
C⁎-simplicity
• Séminaire Bourbaki
• 2020
Furstenberg boundary of minimal actions, Integral Equations
• Operator Theory
• 2020
Furstenberg boundary of minimal actions, Integral Equations Operator Theory
• 2020
Noncommutative Furstenberg boundary
• Mathematics
• 2020
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out to encode
C⁎-simplicity and representations of topological full groups of groupoids
• Mathematics
Journal of Functional Analysis
• 2019
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
C∗-simplicity, Séminaire Bourbaki
• Volume 2018/2019,
• 2019
Essential crossed products for inverse semigroup actions: simplicity and pure infiniteness
• Mathematics
• 2019
We define "essential" crossed products for inverse semigroup actions by Hilbert bimodules on C*-algebras and for Fell bundles over etale, locally compact groupoids. If the underlying groupoid is
Furstenberg Boundary of Minimal Actions
For a countable discrete group $$\Gamma$$ Γ and a minimal $$\Gamma$$ Γ -space X , we study the notion of $$(\Gamma , X)$$ ( Γ , X ) -boundary, which is a natural generalization of the notion of