Operator algebraic characterization of the noncommutative Poisson boundary

Autor:	Houdayer, Cyril
Rok vydání:	2024
Předmět:	Mathematics - Operator Algebras Mathematics - Dynamical Systems Mathematics - Group Theory 20G25 22D25 46L10 46L55
Druh dokumentu:	Working Paper
Popis:	We obtain an operator algebraic characterization of the noncommutative Furstenberg-Poisson boundary $\operatorname{L}(\Gamma) \subset \operatorname{L}(\Gamma \curvearrowright B)$ associated with an admissible probability measure $\mu \in \operatorname{Prob}(\Gamma)$ for which the $(\Gamma, \mu)$-Furstenberg-Poisson boundary $(B, \nu_B)$ is uniquely $\mu$-stationary. This is a noncommutative generalization of Nevo-Sageev's structure theorem [NS11]. We apply this result in combination with previous works to provide further evidence towards Connes' rigidity conjecture for higher rank lattices. Comment: 6 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.11707 Zobrazit plný text záznamu View this record from Arxiv