Geodesic
Partial classification of the Baumslag-Solitar group von Neumann algebras
Documenta mathematica, Tome 19 (2014), pp. 629-645.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: $\noindent $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 $|n'/m'| = |n/m|^{\pm 1}$. 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$_{|n/m|}$.
Classification : 46L36, 20E06, 22D25 
@article{DOCMA_2014__19__a25,
     author = {Meesschaert, Niels and Vaes, Stefaan},
     title = {Partial classification of the {Baumslag-Solitar} group von {Neumann} algebras},
     journal = {Documenta mathematica},
     pages = {629--645},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a25/}
}
TY  - JOUR
AU  - Meesschaert, Niels
AU  - Vaes, Stefaan
TI  - Partial classification of the Baumslag-Solitar group von Neumann algebras
JO  - Documenta mathematica
PY  - 2014
SP  - 629
EP  - 645
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a25/
LA  - en
ID  - DOCMA_2014__19__a25
ER  - 
%0 Journal Article
%A Meesschaert, Niels
%A Vaes, Stefaan
%T Partial classification of the Baumslag-Solitar group von Neumann algebras
%J Documenta mathematica
%D 2014
%P 629-645
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a25/
%G en
%F DOCMA_2014__19__a25
Meesschaert, Niels; Vaes, Stefaan. Partial classification of the Baumslag-Solitar group von Neumann algebras. Documenta mathematica, Tome 19 (2014), pp. 629-645. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a25/