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)

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