The noncommutative factor theorem for lattices in product groups

Abstract

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible lattices $\Gamma <G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $L(\Gamma )\subset M\subset L(\Gamma \curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary.

12 pages. To appear in J. Éc. polytech. Math

References in corpus (2)

• Charmenability of arithmetic groups of product type
• Noncommutative ergodic theory of higher rank lattices

Cited by in corpus (1)

• Operator algebraic characterization of the noncommutative Poisson boundary