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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.

Keywords:  xerox type actions, von Neumann algebras, classification of factors, ergodic equivalence relations

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