TY - JOUR
T1 - Generic dynamics and monotone complete c*-algebras
AU - Sullivan, Dennis
AU - Weiss, B.
AU - Wright, J. D.Maitland
PY - 1986/6
Y1 - 1986/6
N2 - 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.
AB - 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.
KW - Countable group
KW - Dyer factor
KW - Dynamics
KW - Monotone crossproducts
KW - Orbit equivalence
KW - Takenouchi factor
UR - http://www.scopus.com/inward/record.url?scp=84967710244&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1986-0833710-X
DO - 10.1090/S0002-9947-1986-0833710-X
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AN - SCOPUS:84967710244
SN - 0002-9947
VL - 295
SP - 795
EP - 809
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -