A continuous path of singular masas in the hyperfinite II1 factor

• Autores: Allan M. Sinclair, Stuart A. White
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 75, Nº 1, 2007, págs. 243-254
• Idioma: inglés
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• Resumen

  • Using methods of Tauer, we exhibit an uncountable family of singular masas in the hyperfinite II1 factor R all with Pukánszky invariant {1}, no pair of which is conjugate by an automorphism of R. This is done by introducing an invariant (A) for a masa A in a II1 factor N as the maximal size of a projection eA for which A e contains non-trivial centralizing sequences for eN e. The masas produced give rise to a continuous map from the interval [0, 1] into the singular masas in R equipped with the d, 2-metric.

    A result is also given showing that the Pukánszky invariant is d, 2-upper semi-continuous. As a consequence, the sets of masas with Pukánszky invariant {n} are all closed.