Subrelations of ergodic equivalence relations

DOI10.1017/S0143385700004958zbMath0654.22003OpenAlexW2074633401MaRDI QIDQ3800307

Jacob Feldman, Colin E. Sutherland, Robert J. Zimmer

Publication date: 1989

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700004958

zbMATH Keywords

rigidityequivalence relationnormal ergodic subrelationssimple connected non-compact Lie groupamenable relation of type \(II_ 1\)discrete measured equivalence relationsergodic subrelations of finite indexnested pair

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) General groups of measure-preserving transformations (28D15) Discrete subgroups of Lie groups (22E40) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05)

Related Items

Coboundaries of commuting Borel automorphisms ⋮ On orthogonality of two subfactors constructed from factor maps ⋮ Admissible subgroups of full ergodic groups ⋮ Measure equivalence classification of transvection-free right-angled Artin groups ⋮ On the normalizing groupoids and the commensurability groupoids for inclusions of factors associated to ergodic equivalence relations-subrelations ⋮ Suborbits and group extensions of flows ⋮ Stable actions and central extensions ⋮ On sofic groupoids and their full groups ⋮ Lifts of Borel actions on quotient spaces ⋮ Classification of regular subalgebras of injective type III factors ⋮ Groups and dynamics: topology, measure, and Borel structure. Abstracts from the workshop held January 16--22, 2022 ⋮ Symmetric Gibbs measures ⋮ Group cocycles and the ring of affiliated operators ⋮ On extension of cocycles to normalizer elements, outer conjugacy, and related problems ⋮ Inner amenable groups having no stable action ⋮ INNER AMENABLE GROUPOIDS AND CENTRAL SEQUENCES ⋮ Groups generating transversals to semisimple Lie group actions ⋮ Cuntz-Krieger algebras representations from orbits of interval maps ⋮ Examples and properties of nonexact ergodic shift measures ⋮ Prime \(\mathrm{II}_1\) factors arising from irreducible lattices in products of rank one simple Lie groups ⋮ Examples of amalgamated free products and coupling rigidity ⋮ Measure equivalence rigidity of the mapping class group ⋮ Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity ⋮ Hecke von Neumann algebra of ergodic discrete measured equivalence relations ⋮ Invariants of orbit equivalence relations and Baumslag-Solitar groups ⋮ Simple and large equivalence relations ⋮ Cohomology of hyperfinite Borel actions ⋮ Classification of regular subalgebras of the hyperfinite II\(_1\) factor ⋮ Subequivalence relations and positive-definite functions ⋮ Global aspects of measure preserving equivalence relations and graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Ergodic theory, semisimple Lie groups, and foliations by manifolds of negative curvature
• Groups of measure space transformations and invariants of outer conjugation for automorphisms from normalizers of type III full groups
• Action of discrete amenable groups on von Neumann algebras
• Finiteness of quotient groups of discrete subgroups
• Normal ergodic actions
• Index for subfactors
• Transformation groups and \(C^ *\)-algebras
• Fibrations of groupoids
• Virtual groups and group actions
• Geodesic flows on negatively curved manifolds. I
• Borel Structure in Groups and Their Duals
• On Groups of Measure Preserving Transformations. I
• Property T for von Neumann Algebras
• Infinite-dimensional group representations
• On Groups of Measure Preserving Transformations. II