I will discuss a recent joint work with Adrian Ioana (UCSD) in which we recover the Weyl group of a noncompact semisimple algebraic group from natural inclusions of von Neumann algebras arising from algebraic homogeneous actions of irreducible lattices. Our main theorem is a noncommutative analogue of a rigidity result of Bader-Furman-Gorodnik-Weiss (2012) for group actions on algebraic homogeneous spaces and moreover gives new insight towards Connes' rigidity conjecture for higher rank lattices.