On quasi-homomorphism rigidity for lattices in simple algebraic groups

2024/03/25 by Guillaume Dumas, Dumas, Guillaume
Mathematics · Computer Science · #Finite Group Theory Research #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2403.16500

Abstract

Property (TTT) was introduced by Ozawa as a strengthening of Kazhdan's property (T) and Burger and Monod's property (TT). In this paper, we improve Ozawa's result by showing that any simple algebraic group of rank ≥ 2 over a local field has property (TTT). We also show that lattices in a second countable locally compact group inherits property (TTT). Finally, we study to what extent Lie groups with infinite center fail to have properties (TT) and (TTT).

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