We obtain new Bass-Serre-type rigidity results for equivalence relations and their von Neumann algebras, coming from free ergodic actions of free products of groups on the standard probability space. As an application, we show that any nonamenable factor arising as an amalgamated free product of von Neumann algebras over an abelian von Neumann algebra is prime, that is, cannot be written as a tensor product of diffuse factors. This gives, both in the type and in the type cases, new examples of prime factors.
Ionut Chifan. Cyril Houdayer. "Bass-Serre rigidity results in von Neumann algebras." Duke Math. J. 153 (1) 23 - 54, 15 May 2010. https://doi.org/10.1215/00127094-2010-020