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

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
217
Issue
2
Identifiers
DOI: 10.1016/j.aim.2007.09.006
Keywords
  • Generalized Bernoulli Actions
  • Orbit Equivalence
  • Cocycles
  • [Formula Omitted]Factors
  • Outer Automorphism Group

Abstract

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.

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