Operator algebraic characterization of the noncommutative Poisson boundary - Houdayer, Cyril (Comptes Rendus. Mathématique, 2025)
We obtain an operator algebraic characterization of the noncommutative Furstenberg–Poisson boundary $L(Γ ) \subset L(Γ \curvearrowright B)$ associated with an admissible probability measure $μ \in Prob(Γ )$ for which the $(Γ , μ )$-Furstenberg–Poisson boundary $(B, ν _B)$ is uniquely $μ $-stationary. This is a noncommutative generalization of Nevo–Sageev’s structure theorem [14]. We apply this result in combination with previous works to provide further evidence towards Connes’ rigidity conjecture for higher rank lattices.