Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. II
Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. II
Let R be a Borel equivalence relation with countable equivalence classes, on the standard Borel space $(X,\mathcal {A},\mu )$. Let $\sigma$ be a 2-cohomology class on R with values in the torus $\mathbb {T}$. We construct a factor von Neumann algebra ${\mathbf {M}}(R,\sigma )$, generalizing the group-measure space construction of …