Rigidity of free product von Neumann algebras

Cyril Houdayer, Yoshimichi Ueda

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let be any nonempty set and (M i , φi)i∈I let be any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class C anti-free of (possibly type ) von Neumann algebras including all nonprime factors, all nonfull factors and all factors possessing Cartan subalgebras. For the free product (M , φ) =i∈I (M i φi), we show that the free product von Neumann algebra M retains the cardinality [I] and each nonamenable factor M i up to stably inner conjugacy, after permutation of the indices. Our main theorem unifies all previous Kurosh-type rigidity results for free product type II 1 factors and is new for free product type III factors. It moreover provides new rigidity phenomena for type III factors.

Original languageEnglish
Pages (from-to)2461-2492
Number of pages32
JournalCompositio Mathematica
Volume152
Issue number12
DOIs
Publication statusPublished - Dec 1 2016

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Free Product
Von Neumann Algebra
Rigidity
Cartan Subalgebra
Conjugacy
Faithful
Cardinality
Permutation
Arbitrary
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Rigidity of free product von Neumann algebras. / Houdayer, Cyril; Ueda, Yoshimichi.

In: Compositio Mathematica, Vol. 152, No. 12, 01.12.2016, p. 2461-2492.

Research output: Contribution to journalArticle

Houdayer, Cyril ; Ueda, Yoshimichi. / Rigidity of free product von Neumann algebras. In: Compositio Mathematica. 2016 ; Vol. 152, No. 12. pp. 2461-2492.
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