IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
The classifiaction problem for von Neumann algebras
Autor/es:
ROMAN SASYK, ASGER TORNQUIST
Revista:
JOURNAL OF FUNCTIONAL ANALYSIS
Editorial:
Elsevier Inc.
Referencias:
Año: 2009 vol. 256 p. 2710 - 2710
ISSN:
0022-1236
Resumen:
We prove that it is not possible to classify separable von Neumann factors of types $II_1$, $II_infty$  or $III_lambda$, $0 leq lambda leq 1$, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type $II_1$ factors is not smooth. We also prove that the isomorphism relation for von Neumann $II_1$ factors is analytic, but is not Borel.