Modular actions and amenable representations
نویسندگان
چکیده
منابع مشابه
Modular Actions and Amenable Representations
Consider a measure-preserving action Γ y (X,μ) of a countable group Γ and a measurable cocycle α : X × Γ → Aut(Y ) with countable image, where (X,μ) is a standard Lebesgue space and (Y, ν) is any probability space. We prove that if the Koopman representation associated to the action Γ y X is non-amenable, then there does not exist a countable-to-one Borel homomorphism from the orbit equivalence...
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We will give a brief account of (topological) amenable actions and exactness for countable discrete groups. The class of exact groups contains most of the familiar groups and yet is manageable enough to provide interesting applications in geometric topology, von Neumann algebras and ergodic theory. Mathematics Subject Classification (2000). Primary 46L35; Secondary 20F65, 37A20, 43A07.
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Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known as amenability. Amenable objects like groups, semigroups, algebras, graphs, metric spaces, operator algebras etc. play an important role in different areas of mathematics. A big progress in understanding of th...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2009
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-09-04525-5