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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generic dynamics and monotone complete $ C\sp \ast$-algebras


Authors: Dennis Sullivan, B. Weiss and J. D. Maitland Wright
Journal: Trans. Amer. Math. Soc. 295 (1986), 795-809
MSC: Primary 46L55; Secondary 46L35, 54H20
MathSciNet review: 833710
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Abstract: Let $ R$ be any ergodic, countable generic equivalence relation on a perfect Polish space $ X$. It follows from the main theorem of $ \S1$ that, modulo a meagre subset of $ X,R$ may be identified with the relation of orbit equivalence ensuing from a canonical action of $ {\mathbf{Z}}$.

Answering a longstanding problem of Kaplansky, Takenouchi and Dyer independently gave cross-product constructions of Type III $ A{W^\ast}$-factors which were not von Neumann algebras. As a specialization of a much more general result, obtained in $ \S3$, we show that the Dyer factor is isomorphic to the Takenouchi factor.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833710-X
PII: S 0002-9947(1986)0833710-X
Keywords: Dynamics, orbit equivalence, countable group, monotone crossproducts, groupoid $ AW^\ast$-algebras, Takenouchi factor, Dyer factor
Article copyright: © Copyright 1986 American Mathematical Society