منابع مشابه
Ergodic Theorems for Actions of Hyperbolic Groups
In this note we give a short proof of a pointwise ergodic theorem for measure preserving actions of word hyperbolic groups, also obtained recently by Bufetov, Khristoforov and Klimenko. Our approach also applies to infinite measure spaces and one application is to linear actions of discrete groups on the plane. 0. Introduction The well-known Birkhoff ergodic theorem for ergodic transformations ...
متن کاملErgodic Actions of Universal Quantum Groups on Operator Algebras
We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...
متن کاملCocycle Superrigidity for Ergodic Actions of Non-semisimple Lie Groups
Suppose L is a semisimple Levi subgroup of a connected Lie group G, X is a Borel G-space with finite invariant measure, and α : X × G → GLn(R) is a Borel cocycle. Assume L has finite center, and that the real rank of every simple factor of L is at least two. We show that if L is ergodic on X, and the restriction of α to X × L is cohomologous to a homomorphism (modulo a compact group), then, aft...
متن کاملErgodic Actions of Countable Groups and Finite Generating Partitions
We prove the following finite generator theorem. Let G be a countable group acting ergodically on a standard probability space. Suppose this action admits a generating partition having finite Shannon entropy. Then the action admits a finite generating partition. We also discuss relationships between generating partitions and f-invariant and sofic entropies.
متن کاملErgodic Actions of Semisimple Lie Groups on Compact Principal Bundles
Let G = SL(n, R) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M , such that there is a volume-preserving, connection-preserving, ergodic action of G on some smooth, principal K-bundle P over M. Can M can be chosen independent of K? We show that if M = H / A is a homogeneous space, and the action of G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1977
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1977.70.519