A continuous path of singular masas in the hyperfinite II1 factor
نویسندگان
چکیده
Using methods of R.J.Tauer [13] we exhibit an uncountable family of singular masas in the hyperfinite II1 factor R all with Pukánszky invariant {1}, no pair of which are conjugate by an automorphism of R. This is done by introducing an invariant Γ(A) for a masa A in a II1 factor N as the maximal size of a projection e ∈ A for which Ae contains non-trivial centralising sequences for eNe. The masas produced give rise to a continuous map from the interval [0, 1] into the singular masas in R equiped with the d∞,2-metric. A result is also given showing that the Pukánszky invariant [11] is d∞,2-upper semi-continuous. As a consequence, the sets of masas with Pukánszky invariant {n} are all closed.
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