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 II<sub>1</sub> 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 II<sub>1</sub> factor containing a masa with Pukánszky invariant {1}. In particular the hyperfinite II<sub>1</sub> factor and all separable McDuff II<sub>1</sub> factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff II<sub>1</sub> factor we show that every subset of the N ∪ {∞} containing ∞ is obtained as a Pukánszky invariant of some masa.
Item Type: | Articles |
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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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