L^2-Homology for von Neumann Algebras
| dc.creator | Connes, Alain | |
| dc.creator | Shlyakhtenko, Dimitri | |
| dc.date | 2003-09-20 | |
| dc.date.accessioned | 2026-07-07T05:01:20Z | |
| dc.date.available | 2026-07-07T05:01:20Z | |
| dc.description | We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these invariants is obtained from the definition of L^2 homology for groups, using the ideas from the theory of correspondences. For the group algebra of a discrete group, our Betti numbers coincide with the L^2 Betti numbers of the group. We find a link between the first L^2 Betti number and free entropy dimension, which points to the non-vanishing of L^2 homology for the von Neumann algebra of a free group. | |
| dc.identifier | https://arxiv.org/abs/math/0309343 | |
| dc.identifier | http://arxiv.org/abs/math/0309343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68631 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10; 46L54 | |
| dc.title | L^2-Homology for von Neumann Algebras | |
| dc.type | text |