Partial classification of the Baumslag-Solitar group von Neumann algebras
Operator Algebras
2014-08-04 v3 Group Theory
Abstract
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| or |m/n|. We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II_1 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|.
Keywords
Cite
@article{arxiv.1301.0510,
title = {Partial classification of the Baumslag-Solitar group von Neumann algebras},
author = {Niels Meesschaert and Stefaan Vaes},
journal= {arXiv preprint arXiv:1301.0510},
year = {2014}
}
Comments
v2: only minor changes. v3: minor changes, final version, to appear in Documenta Mathematica