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2014 Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups
Sorin Popa, Stefaan Vaes
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Acta Math. 212(1): 141-198 (2014). DOI: 10.1007/s11511-014-0110-9

Abstract

We prove that for any free ergodic probability measure-preserving action Fn(X,μ) of a free group on n generators Fn,2n, the associated group measure space II1 factor L(X)Fn has L(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II1 factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II1 factors arising from arbitrary actions of a much larger family of groups, including all free products of amenable groups and their direct products.

Funding Statement

S.P. was supported in part by NSF Grant DMS-1101718. S.V. was supported by ERC Starting Grant VNALG-200749, Research Programme G.0639.11 of the Research Foundation – Flanders (FWO) and KU Leuven BOF research grant OT/08/032.

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Sorin Popa. Stefaan Vaes. "Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups." Acta Math. 212 (1) 141 - 198, 2014. https://doi.org/10.1007/s11511-014-0110-9

Information

Received: 13 June 2012; Published: 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1307.46047
MathSciNet: MR3179609
Digital Object Identifier: 10.1007/s11511-014-0110-9

Rights: 2014 © Institut Mittag-Leffler

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Vol.212 • No. 1 • 2014
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