Unique prime decomposition results for factors coming from wreath product groups

J. Owen Sizemore and Adam Winchester

Vol. 265 (2013), No. 1, 221–232

DOI: 10.2140/pjm.2013.265.221

Abstract

We use malleable deformations combined with spectral gap rigidity theory, in the framework of Popa’s deformation/rigidity theory, to prove unique tensor product decomposition results for II₁ factors arising as tensor products of wreath product factors. We also obtain a similar result regarding measure equivalence decomposition of direct products of such groups.

Keywords

operator algebras, measure equivalence, group theory

Mathematical Subject Classification 2010

Primary: 47L65, 46L36

Milestones

Received: 19 October 2011

Revised: 26 January 2013

Accepted: 3 July 2013

Published: 28 August 2013