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- W771103721 abstract "Let $I$ be any nonempty set and $(M_i, varphi_i)_{i in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $mathcal C_{rm anti-free}$ of (possibly type III) von Neumann algebras including all nonprime factors, all nonfull factors and all factors possessing a Cartan subalgebra. For the free product $(M, varphi) = ast_{i in I} (M_i, varphi_i)$, 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." @default.
- W771103721 created "2016-06-24" @default.
- W771103721 creator A5000473085 @default.
- W771103721 creator A5084037236 @default.
- W771103721 date "2016-11-17" @default.
- W771103721 modified "2023-10-14" @default.
- W771103721 title "Rigidity of free product von Neumann algebras" @default.
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- W771103721 doi "https://doi.org/10.1112/s0010437x16007673" @default.
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