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...

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Detalles Bibliográficos
Autores: Sasyk, Roman, Törnquist, Asger
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
Descripción
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.