Let be any nonempty set and (Mi, φi)i∈I let be any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class Canti-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 (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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory