Resumen de A note on the classification of gamma factors

Román Sasyk

• One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. The set of separable II1 factors can be split in two disjoint subsets: those that have the property Gamma and those that do not have it, called full factors by Connes. In this note we prove that it is not possible to classify separable II1 factors satisfying the property Gamma up to isomorphism by a Borel measurable assignment of countable structures as invariants. We also show that the same holds true for the full II1 factors.