On minimal, strongly proximal actions of locally compact groups

DOI10.1007/BF02807197zbMath1037.22013OpenAlexW1975960803WikidataQ126208751 ScholiaQ126208751MaRDI QIDQ1424108

Alex Furman

Publication date: 8 March 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02807197

zbMATH Keywords

Hilbert-Smith conjectureboundary actionsstrongly proximal actions

Mathematics Subject Classification ID

Ergodic theory on groups (22D40)

Related Items (22)

Noncommutative Furstenberg boundary ⋮ Topological Boundaries of Unitary Representations ⋮ Boundaries of reduced \(C^\ast\)-algebras of discrete groups ⋮ Boundary maps and covariant representations ⋮ On invariant subalgebras of group and von Neumann algebras ⋮ Arboreal structures on groups and the associated boundaries ⋮ Piecewise strongly proximal actions, free boundaries and the Neretin groups ⋮ Stationary \(C^\ast \)-dynamical systems (with an appendix by Uri Bader, Yair Hartman, and Mehrdad Kalantar) ⋮ Gelfand pairs admit an Iwasawa decomposition ⋮ Amenable uniformly recurrent subgroups and lattice embeddings ⋮ \(C^*\)-simplicity and the unique trace property for discrete groups ⋮ Subgroup dynamics and $C^\ast$-simplicity of groups of homeomorphisms ⋮ \(C^*\)-simplicity of HNN extensions and groups acting on trees ⋮ Normal amenable subgroups of the automorphism group of sofic shifts ⋮ Lattice envelopes ⋮ Boundary maps, germs and quasi-regular representations ⋮ Bounding the covolume of lattices in products ⋮ Thompson’s group is not strongly amenable ⋮ Strong amenability and the infinite conjugacy class property ⋮ A weak expectation property for operator modules, injectivity and amenable actions ⋮ A New Look at C∗-Simplicity and the Unique Trace Property of a Group ⋮ Normal amenable subgroups of the automorphism group of the full shift

Cites Work

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• Pinching constants for hyperbolic manifolds
• Proximal flows
• Groups acting on the circle.
• A Poisson formula for semi-simple Lie groups
• The Hilbert-Smith conjecture for Hölder actions
• The Hilbert-Smith conjecture for quasiconformal actions
• Mostow-Margulis rigidity with locally compact targets

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