Generic dynamics and monotone complete c*-algebras

Dennis Sullivan, B. Weiss, J. D.Maitland Wright

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

Let R be any ergodic, countable generic equivalence relation on a perfect Polish space X. It follows from the main theorem of §1 that, modulo a meagre subset of X, R may be identified with the relation of orbit equivalence ensuing from a canonical action of Z. Answering a longstanding problem of Kaplansky, Takenouchi and Dyer independently gave cross-product constructions of Type III AW*-factors which were not von Neumann algebras. As a specialization of a much more general result, obtained in §3, we show that the Dyer factor is isomorphic to the Takenouchi factor.

Original languageEnglish
Pages (from-to)795-809
Number of pages15
JournalTransactions of the American Mathematical Society
Volume295
Issue number2
DOIs
StatePublished - Jun 1986

Keywords

  • Countable group
  • Dyer factor
  • Dynamics
  • Monotone crossproducts
  • Orbit equivalence
  • Takenouchi factor

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