A type I conjecture and boundary representations of hyperbolic groups
DOI10.1112/plms.12547zbMath1527.22009arXiv2110.00190OpenAlexW3202135029WikidataQ123237772 ScholiaQ123237772MaRDI QIDQ6075104
Mehrdad Kalantar, Nicolas Monod, Pierre-Emmanuel Caprace
Publication date: 20 September 2023
Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2110.00190
representationlocally compact grouphyperbolic grouplength function\(C^{\ast}\)-algebracocompact subgrouptype I group
General theory of (C^*)-algebras (46L05) Unitary representations of locally compact groups (22D10) Hyperbolic groups and nonpositively curved groups (20F67) General properties and structure of locally compact groups (22D05) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Groups acting on trees (20E08) Means on groups, semigroups, etc.; amenable groups (43A07)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Relative amenability
- Boundary unitary representations -- irreducibility and rigidity
- Simple locally compact groups acting on trees and their germs of automorphisms.
- \(C^*\)-simplicity of locally compact Powers groups
- \(C^*\)-simplicity and the unique trace property for discrete groups
- Arithmetic subgroups of algebraic groups
- Amenable hyperbolic groups
- An indiscrete Bieberbach theorem: from amenable \(\mathrm{CAT}(0)\) groups to Tits buildings
- A characterization of higher rank symmetric spaces via bounded cohomology
- Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
- Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
- Proximal flows
- Groups of isometries of a tree and the CCR property
- Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
- Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups
- Continuous bounded cohomology and applications to rigidity theory
- On spectra of Koopman, groupoid and quasi-regular representations
- Uniformly recurrent subgroups and simple \(C^{\ast}\)-algebras
- Hyperbolic groups have flat-rank at most 1
- Boundary maps, germs and quasi-regular representations
- Gelfand pairs admit an Iwasawa decomposition
- On spectral characterizations of amenability
- Fixed points and amenability in non-positive curvature
- Boundaries of reduced \(C^\ast\)-algebras of discrete groups
- Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras
- Über unitäre Darstellungen abzählbarer, diskreter Gruppen
- Type I \(C^ *\)-algebras
- Eine Charakterisierung diskreter Gruppen vom Typ I
- Moyennes invariantes et représentations unitaires
- Certain topological groups are type I. II
- Uniformly recurrent subgroups
- A Course in Abstract Harmonic Analysis
- Uniform Tree Lattices
- Isometry groups of non-positively curved spaces: structure theory
- On simplicity of reduced C*-algebras of groups
- Amenable Actions and Weak Containment of Certain Representations of Discrete Groups
- Cocompact Amenable Closed Subgroups: Weakly Inequivalent Representations in the Left-Regular Representation
- Subgroup dynamics and $C^\ast$-simplicity of groups of homeomorphisms
- Unitary Representations of Groups, Duals, and Characters
- Reduction of cocycles with hyperbolic targets
- Positive Definite Measures
- Groups of Automorphisms of Borel Spaces
- Weak Containment and Induced Representations of Groups
- Unitary representations of solvable Lie groups
- Über das Haarsche Mass in der lokal bikompakten Gruppe
- Principles of harmonic analysis
- Continuous bounded cohomology of locally compact groups
- A theorem on unitary representations of semisimple Lie groups