The classification problem for von Neumann factors

Roman Sasyk; Asger Tornquist

The classification problem for von Neumann factors

Operator Algebras 2009-03-27 v1 Logic

Authors: Roman Sasyk , Asger Tornquist

Abstract

We prove that it is not possible to classify separable von Neumann factors of types $\II_1$ , $\II_\infty$ or $\III_\lambda$ , $0\leq \lambda\leq1$ , 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.

Keywords

von neumann algebras

Cite

@article{arxiv.0903.4484,
  title  = {The classification problem for von Neumann factors},
  author = {Roman Sasyk and Asger Tornquist},
  journal= {arXiv preprint arXiv:0903.4484},
  year   = {2009}
}

Comments

To appear in the Journal of Functional Analysis

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