Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan’s property (T)

DOI10.1090/S0002-9947-99-02363-6zbMath0932.22007MaRDI QIDQ4243650

Yehuda Shalom

Publication date: 19 May 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

linear algebraic groupsalgebraic varietiesfinitely-additive measures\(k\)-amenableproperty \((T)\) of Kazhdan

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) General groups of measure-preserving transformations (28D15) Analysis on (p)-adic Lie groups (22E35)

Related Items

Property (T) for fiber products ⋮ A joinings classification and a special case of Raghunathan's conjecture in positive characteristic (with an appendix by Kevin Wortman) ⋮ Diagonal actions in positive characteristic ⋮ Charmenability of higher rank arithmetic groups ⋮ \(\operatorname{SL}_2\) representations and relative property (T) ⋮ Rigidity for group actions on homogeneous spaces by affine transformations ⋮ Presentability by products for some classes of groups ⋮ Rigid geometric structures, isometric actions, and algebraic quotients ⋮ Strong relative property \((T)\) and spectral gap of random walks ⋮ The product replacement algorithm and Kazhdan’s property (T) ⋮ Kazhdan constants for conjugacy classes of compact groups. ⋮ Stabilizer rigidity in irreducible group actions ⋮ Measure expanding actions, expanders and warped cones ⋮ Characteristic free measure rigidity for the action of solvable groups on homogeneous spaces ⋮ A characterization of relative Kazhdan property T for semidirect products with abelian groups ⋮ Rigidity of group actions on homogeneous spaces. III ⋮ Applications of Kazhdan's property (T) to automatic continuity ⋮ Relative property (T) for the subequivalence relations induced by the action of SL\(_2(\mathbb Z)\) on \(\mathbb T^2\) ⋮ The Plancherel formula for countable groups ⋮ Kazhdan projections, random walks and ergodic theorems ⋮ Quasi-homomorphism rigidity with non-commutative targets ⋮ A full description of property \(T\) of unital \(C^\ast\)-crossed products ⋮ An embedding theorem for automorphism groups of Cartan geometries ⋮ Explicit Kazhdan constants for representations of semisimple and arithmetic groups ⋮ Relative Kazhdan Property ⋮ BOREL DENSITY FOR APPROXIMATE LATTICES ⋮ Identity excluding groups ⋮ Property \(T\) of group homomorphisms ⋮ Invariant random subgroups of linear groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Density properties for certain subgroups of semi-simple groups without compact components
• On ergodic quasi-invariant measures of group automorphism
• Kazhdan groups acting on compact manifolds
• Zariski density in Lie groups
• Some remarks on invariant means
• A simple proof of Borel's density theorem
• Property T and asymptotically invariant sequences
• On the density theorems of Borel und Furstenberg
• Expanding graphs and invariant means
• Arithmetic lattices and commensurator according to G. A. Margulis
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\)
• Superrigidity of lattices in solvable Lie groups
• Algebraic hulls and the Følner property
• Théoremes de finitude en cohomologie galoisienne
• Connection of the dual space of a group with the structure of its closed subgroups
• Amenable actions of locally compact groups
• Kazhdan constants for SL (3, Z).
• Hecke operators and distributing points on S². II
• For 𝑛>3 there is only one finitely additive rotationally invariant measure on the 𝑛-sphere defined on all Lebesgue measurable subsets
• Uniqueness of Invariant Means for Measure-Preserving Transformations
• On Anisotropic Solvable Linear Algebraic Groups
• Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
• Elementary proof of a theorem of Bruhat-Tits-Rousseau and of a theorem of Tits
• Invariant Geometric Structures: A Non-Linear Extension of the Borel Density Theorem
• A Note on Borel's Density Theorem
• On the Mautner Phenomenon and Groups with Property (T)