Rigidity of Furstenberg entropy for semisimple Lie group actions

DOI10.1016/S0012-9593(00)00113-0zbMath0956.22005OpenAlexW2080433018WikidataQ115340631 ScholiaQ115340631MaRDI QIDQ4502946

Robert J. Zimmer, Amos Nevo

Publication date: 7 March 2001

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2000_4_33_3_321_0

zbMATH Keywords

parabolic subgroupsrigiditysemisimple Lie groupstationary measuresFurstenberg entropy

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Ergodic theory on groups (22D40) General groups of measure-preserving transformations (28D15) Boundary theory for Markov processes (60J50) Variational aspects of group actions in infinite-dimensional spaces (58E40) Noncompact Lie groups of transformations (57S20)

Related Items

Factor and normal subgroup theorems for lattices in products of groups, Property (T) and the Furstenberg entropy of nonsingular actions, Furstenberg entropy values for nonsingular actions of groups without property (T), Boundaries of dense subgroups of totally disconnected groups, Kudō-continuity of conditional entropies, Generic stationary measures and actions, Random walks on random coset spaces with applications to Furstenberg entropy, Stationary characters on lattices of semisimple Lie groups, A generalization of the intermediate factors theorem, Boundary entropy spectra as finite subsums, Invariant rigid geometric structures and smooth projective factors, Furstenberg entropy of intersectional invariant random subgroups, Rigidity of Furstenberg entropy for semisimple Lie group actions, Furstenberg entropy realizations for virtually free groups and lamplighter groups

Cites Work

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• Ergodic theory, semisimple Lie groups, and foliations by manifolds of negative curvature
• A generalization of the intermediate factors theorem
• Random walks on discrete groups: Boundary and entropy
• Propriétés de contraction d'un semi-groupe de matrices inversibles. Coefficients de Liapunoff d'un produit de matrices aléatoires indépendantes. (Contraction properties of a semigoup of invertible matrices. Lyapunov coefficient of a product of independent random matrices)
• On the cohomology of ergodic group actions
• Homogeneous projective factors for actions of semi-simple Lie groups
• Free quotients and the first Betti number of some hyperbolic manifolds
• A Poisson formula for semi-simple Lie groups
• Representations of Fundamental Groups of Manifolds with a Semisimple Transformation Group
• Induced and amenable ergodic actions of Lie groups
• Topological superrigidity and anosov actions of lattices
• Rigidity of Furstenberg entropy for semisimple Lie group actions
• Noncommuting Random Products
• Arithmetic structure of fundamental groups and actions of semisimple Lie groups