Values of the Pukánszky invariant in McDuff factors

White, S.A. (2008) Values of the Pukánszky invariant in McDuff factors. Journal of Functional Analysis, 254(3), pp. 612-631. (doi:10.1016/j.jfa.2007.10.011)

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Publisher's URL: http://dx.doi.org/10.1016/j.jfa.2007.10.011

Abstract

In 1960 Pukánszky introduced an invariant associating to every masa in a separable II1 factor a non-empty subset of the N ∪ {∞}. This invariant examines the multiplicity structure of the von Neumann algebra generated by the left-right action of the masa. In this paper it is shown that any non-empty subset of the N ∪ {∞} arises as the Pukánszky invariant of some masa in a separable McDuff II1 factor containing a masa with Pukánszky invariant {1}. In particular the hyperfinite II1 factor and all separable McDuff II1 factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff II1 factor we show that every subset of the N ∪ {∞} containing ∞ is obtained as a Pukánszky invariant of some masa.

Item Type:Articles
Keywords:Pukánszky invariant; Masa; McDuff factor
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: 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 Functional Analysis
Publisher:Elsevier
ISSN:0022-1236
Copyright Holders:Copyright © 2007 Elsevier
First Published:First published in Journal of Functional Analysis 254(3):612-631
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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