Geodesic
Partial classification of the Baumslag-Solitar group von Neumann algebras
Documenta mathematica, Tome 19 (2014), pp. 629-645
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We prove that the rational number ∣n/m∣ is an invariant of the group von Neumann algebra of the Baumslag–Solitar group BS(n,m). More precisely, if L(BS(n,m)) is isomorphic with L(BS(n′,m′)), then ∣n′/m′∣=∣n/m∣±1. We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II1​ factor, an equivalence relation that can be of type III. In particular, we associate to L(BS(n,m)) a canonical equivalence relation of type III∣n/m∣​.
DOI : 10.4171/dm/458
Classification : 20E06, 22D25, 46L36 
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     author = {Stefaan Vaes and Niels Meesschaert},
     title = {Partial classification of the {Baumslag-Solitar} group von {Neumann} algebras},
     journal = {Documenta mathematica},
     pages = {629--645},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/458},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/458/}
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Stefaan Vaes; Niels Meesschaert. Partial classification of the Baumslag-Solitar group von Neumann algebras. Documenta mathematica, Tome 19 (2014), pp. 629-645. doi: 10.4171/dm/458

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