The classification problem for von Neumann factors
We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the is...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/19477 |
| Acceso en línea: | http://hdl.handle.net/11336/19477 |
| Access Level: | acceso abierto |
| Palabra clave: | von Neumann algebras Classification Borel reducibility Turbulence https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel. |
|---|