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II1 FACTORS WITH EXOTIC CENTRAL SEQUENCE ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  19 December 2019

Adrian Ioana Open the ORCID record for Adrian Ioana [Opens in a new window]  and
Pieter Spaas
Adrian Ioana
Affiliation:
Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA (aioana@ucsd.edu; pspaas@ucsd.edu)
Pieter Spaas
Affiliation:
Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA (aioana@ucsd.edu; pspaas@ucsd.edu)
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Abstract

We provide a class of separable II1 factors $M$ whose central sequence algebra is not the ‘tail’ algebra associated with any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff [On residual sequences in a II1 factor, J. Lond. Math. Soc. (2) (1971), 273–280].

Keywords

II1 factorcentral sequence algebraresidual sequenceGaussian actiontracial stabilitydeformation rigidity theory

MSC classification

Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L36: Classification of factors
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 5 , September 2021 , pp. 1671 - 1696
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Copyright
© Cambridge University Press 2019

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Footnotes

The authors were supported in part by NSF Career Grant DMS #1253402.

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