Strange factor representations of type II1 and pairs of dual dynamical systems
Abstract
Given a pair of dynamical systems we consider a pair of commuting von Neumann factors of type 111. The construction is a generalization of classical von Neumann-Murrey and grouppoid construction. It gives a natural examples of factors with non-unit coupling constant.As the partial cases we obtain Connes-Riffel-Faddeev examples of the representations of rotation algebra. We give also an example for infinite symmetric group.
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