Kyoto Journal of Mathematics

Constructing MASAs with prescribed properties

Sorin Popa

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Abstract

We consider an iterative procedure for constructing maximal abelian -subalgebras (MASAs) satisfying prescribed properties in II1 factors. This method pairs well with the intertwining by bimodules technique and with properties of the MASA and of the ambient factor that can be described locally. We obtain such a local characterization for II1 factors M that have an s-MASA, AM (i.e., for which AJAJ is maximal abelian in B(L2M)), and use this strategy to prove that any factor in this class has uncountably many nonintertwinable singular (resp., semiregular) s-MASAs.

Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 367-397.

Dates
Received: 11 December 2016
Revised: 5 March 2017
Accepted: 9 March 2017
First available in Project Euclid: 27 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1551236641

Digital Object Identifier
doi:10.1215/21562261-2019-0003

Mathematical Reviews number (MathSciNet)
MR3960298

Zentralblatt MATH identifier
07080109

Subjects
Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L36: Classification of factors 46L37: Subfactors and their classification

Keywords
II$_{1}$ factor singular MASA semiregular MASA s-thin approximation

Citation

Popa, Sorin. Constructing MASAs with prescribed properties. Kyoto J. Math. 59 (2019), no. 2, 367--397. doi:10.1215/21562261-2019-0003. https://projecteuclid.org/euclid.kjm/1551236641


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