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1 October 2021 Coarse decomposition of II1 factors
Sorin Popa
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Duke Math. J. 170(14): 3073-3110 (1 October 2021). DOI: 10.1215/00127094-2021-0059

Abstract

We prove that any separable II1 factor M admits a coarse decomposition over the hyperfinite II1 factor R—that is, there exists an embedding RM such that L2ML2R is a multiple of the coarse Hilbert R-bimodule L2RL2Rop. Equivalently, the von Neumann algebra generated by left and right multiplication by R on L2ML2R is isomorphic to RRop. Moreover, if QM is an infinite-index irreducible subfactor, then RM can be constructed to be coarse with respect to Q as well. This implies the existence of maximal abelian -subalgebras that are mixing, strongly malnormal, and with infinite multiplicity, in any given separable II1 factor.

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Sorin Popa. "Coarse decomposition of II1 factors." Duke Math. J. 170 (14) 3073 - 3110, 1 October 2021. https://doi.org/10.1215/00127094-2021-0059

Information

Received: 31 May 2020; Revised: 18 October 2020; Published: 1 October 2021
First available in Project Euclid: 10 September 2021

Digital Object Identifier: 10.1215/00127094-2021-0059

Subjects:
Primary: 46L10
Secondary: 46L30 , 46L36 , 46L55

Keywords: coarse decomposition , hyperfinite factors , II1 factors , maximal abelian *-subalgebras

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 14 • 1 October 2021
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