Partial classification of the Baumslag-Solitar group von Neumann algebras

  • Niels Meesschaert

  • Stefaan Vaes

    Leuven Department of Mathematics Department of Mathematics Leuven (Belgium) Leuven (Belgium
Partial classification of the Baumslag-Solitar group von Neumann algebras cover
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Abstract

We prove that the rational number is an invariant of the group von Neumann algebra of the Baumslag–Solitar group . More precisely, if is isomorphic with , then . We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II factor, an equivalence relation that can be of type III. In particular, we associate to a canonical equivalence relation of type III.

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Niels Meesschaert, Stefaan Vaes, Partial classification of the Baumslag-Solitar group von Neumann algebras. Doc. Math. 19 (2014), pp. 629–645

DOI 10.4171/DM/458