Journal of Operator Theory
Volume 72, Issue 2, Fall 2014 pp. 343-369.
Von Neumann algebras arising as fixed point algebras
under xerox type actions
Authors:
Thierry Giordano (1)
and Radu-B. Munteanu (2)
Author institution: (1) Department of Mathematics and Statistics,
University of Ottawa, Ottawa, K1N 6N5, Canada
(2) Department of Mathematics, Universiy of Bucharest, Bucharest, 010014,
Romania
Summary: In this paper we analyze approximately finite
dimensional von Neumann algebras obtained as weak closure of fixed point
algebras under xerox type action of compact groups on UHF algebras. We
reduce our analysis to the case of diagonal xerox type actions. The von
Neumann algebras that we study are identified with von Neumann algebras
associated to certain hyperfinite equivalence relations. We give conditions
for such von Neumann algebras to be factors and we determine their type.
DOI: http://dx.doi.org/10.7900/jot.2013mar14.1984
Keywords: xerox type actions, von Neumann algebras, classification
of factors, ergodic equivalence relations
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