Generic representations of abelian groups and extreme amenability

DOI10.1007/s11856-013-0036-5zbMath1279.43002arXiv1107.1698OpenAlexW2027918139MaRDI QIDQ375504

Julien Melleray, Todor Tsankov

Publication date: 31 October 2013

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

Full work available at URL: https://arxiv.org/abs/1107.1698

zbMATH Keywords

abelian groupsamenabilityPolish group

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34C99) Means on groups, semigroups, etc.; amenable groups (43A07) Maps and general types of topological spaces defined by maps (54C99) Smooth dynamical systems: general theory (37C99)

Related Items (24)

Metrical universality for groups ⋮ Topological isomorphism for rank-1 systems ⋮ Prolonged analytic connected group actions are generically free ⋮ On some generic classes of ergodic measure preserving transformations ⋮ Group actions: Entropy, mixing, spectra, and generic properties ⋮ Generic norms and metrics on countable abelian groups ⋮ The spectral form of Koopman representations of the group of measurable functions with values in the circle ⋮ Universal actions and representations of locally finite groups on metric spaces ⋮ From isolated subgroups to generic permutation representations ⋮ Generic measure preserving transformations and the closed groups they generate ⋮ Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions ⋮ Unitary representations of the groups of measurable and continuous functions with values in the circle ⋮ Random orderings and unique ergodicity of automorphism groups ⋮ Extensions of generic measure-preserving actions ⋮ The Ramsey property for operator spaces and noncommutative Choquet simplices ⋮ Polish groups and Baire category methods ⋮ Extreme amenability of abelian \(L_0\) groups ⋮ Generic behavior of a measure-preserving transformation ⋮ Fixed points in compactifications and combinatorial counterparts ⋮ Generic representations of countable groups ⋮ Borel functors, interpretations, and strong conceptual completeness for ℒ_{𝜔₁𝜔} ⋮ Amenability and Ramsey theory in the metric setting ⋮ Polish groupoids and functorial complexity ⋮ Higher-dimensional obstructions for star reductions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extensions of generic measure-preserving actions
• On minimal actions of Polish groups
• The generic automorphism of a Lebesgue space conjugate to a \(G\)-extension for any finite abelian group \(G\).
• Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups
• An anti-classification theorem for ergodic measure preserving transformations
• Non-genericity phenomena in ordered Fraïssé classes
• Finitely approximable groups and actions Part II: Generic representations
• Residual Properties of Infinite Soluble Groups
• The generic isometry and measure preserving homeomorphism are conjugate to their powers
• Turbulence, amalgamation, and generic automorphisms of homogeneous structures
• A Topological Application of the Isoperimetric Inequality
• The commutant is the weak closure of the powers, for rank-1 transformations
• Generating Dense Subgroups of Measure Preserving Transformations
• The Small Index Property for ω‐Stable ω‐Categorical Structures and for the Random Graph
• The generic transformation has roots of all orders
• Über die Permutationsgruppe der natürlichen Zahlenfolge
• Closed subgroups generated by generic measure automorphisms
• Turbulence, representations, and trace-preserving actions
• SOME EXTREMELY AMENABLE GROUPS RELATED TO OPERATOR ALGEBRAS AND ERGODIC THEORY
• Commuting point transformations
• [https://portal.mardi4nfdi.de/wiki/Publication:5676460 Entropie d'un groupe ab�lien de transformations]
• Spatial and non-spatial actions of Polish groups

This page was built for publication: Generic representations of abelian groups and extreme amenability