Embedding universality for II1 factors with property (T)

Abstract

We prove that every separable tracial von Neumann algebra embeds into a II1 factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. We also establish an analogous result for the trivial extension over a non-atomic probability space of every countable p.m.p. equivalence relation. In addition, we obtain two new results concerning the structure of infinitely generic II1 factors. These results are obtained by using the class of wreath-like product groups introduced recently in [8].