@article{oai:nagoya.repo.nii.ac.jp:00028447, author = {Houdayer, Cyril and Ueda, Yoshimichi}, issue = {12}, journal = {Compositio Mathematica}, month = {Dec}, note = {Let I be any nonempty set and let (Mi, φi)i∈I be any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class C anti-free of (possibly type III) von Neumann algebras including all nonprime factors, all nonfull factors and all factors possessing Cartan subalgebras. For the free product (M,φ)=*i∈I(Mi,φi) , we show that the free product von Neumann algebra M retains the cardinality |I| and each nonamenable factor Mi up to stably inner conjugacy, after permutation of the indices. Our main theorem unifies all previous Kurosh-type rigidity results for free product type II1 factors and is new for free product type III factors. It moreover provides new rigidity phenomena for type III factors.}, pages = {2461--2492}, title = {Rigidity of free product von Neumann algebras}, volume = {152}, year = {2016} }