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Product Rigidity in Von Neumann and C-Algebras Via S-Malleable Deformations
Journal article   Peer reviewed

Product Rigidity in Von Neumann and C-Algebras Via S-Malleable Deformations

Daniel Drimbe
Communications in mathematical physics, Vol.388(1), pp.329-349
11/01/2021
DOI: 10.1007/s00220-021-04210-y
url
https://arxiv.org/pdf/2012.04089View
Open Access

Abstract

We provide a new large class of countable icc groups A for which the product rigidity result from Chifan et al. (Geom Funct Anal 26(1): 136-159, 2016) holds: if Gamma(1), ..., Gamma(n) is an element of A and Lambda is any group such that L (Gamma(1 )x( )...( ) x Gamma(n)) congruent to L(Lambda), then there exists a product decomposition Lambda = Lambda(1) x ... x Lambda(n) such that L (Lambda(i)) is stably isomorphic to L(Gamma(i)), for any 1 <= i <= n. Class A consists of groups Gamma for which L(Gamma) admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups Gamma such that either (a) Gamma admits an unbounded 1-cocycle into its left regular representation, or (b) Gamma is an arbitrary wreath product group with amenable base. As a byproduct of these results, we obtain new examples of W*-supeffigid groups and new rigidity results in the C*-algebra theory.
Physical Sciences Physics Physics, Mathematical Science & Technology

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