Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups

Abstract

We study equivalence relations and II_1 factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II_1 factors. This yields explicit computations of outer automorphism and fundamental groups. In particular, every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic II_1 factors.

Some remarks added and a few minor corrections made

References in corpus (2)

• Outer automorphism groups of some ergodic equivalence relations
• On the Cohomology of Actions of Groups by Bernoulli Shifts

Cited by in corpus (1)

• Factors of type II_1 without non-trivial finite index subfactors