A continuous path of singular masas in the hyperfinite II₁ factor

Sinclair, A.M. and White, S.A. (2007) A continuous path of singular masas in the hyperfinite II₁ factor. Journal of the London Mathematical Society, 75(1), pp. 243-254. (doi: 10.1112/jlms/jdl019)

Abstract

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 Γ(A) for a masa A in a II₁ factor N as the maximal size of a projection eε A for which A e contains non-trivial centralizing sequences for eNe. 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: White, Professor Stuart
• Authors: Sinclair, A.M., and White, S.A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of the London Mathematical Society
• Publisher: Oxford University Press
• ISSN: 0024-6107
• Published Online: 31 January 2007
• Copyright Holders: Copyright © 2008 Oxford University Press
• First Published: First published in Journal of the London Mathematical Society 75(1):243-251
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher