A relative version of Connes' $χ(M)$ invariant and existence of orbit inequivalent actions
| dc.creator | Ioana, Adrian | |
| dc.date | 2004-11-08 | |
| dc.date | 2006-02-14 | |
| dc.date.accessioned | 2026-07-07T06:38:59Z | |
| dc.date.available | 2026-07-07T06:38:59Z | |
| dc.description | We consider a new orbit equivalence invariant for measure-preserving actions of groups on the probability space, $σ:G\to$ Aut$(X,μ)$, denoted $χ_0(σ;G)$ and defined as the "intersection" of the 1-cohomology group, H$^1(σ,G)$, with Connes' $χ(M)$ invariant of the cross product von Neumann algebra, $M=L^\infty(X,μ)\rtimes_σG$. We calculate $χ_0(σ;G)$ for certain actions of groups of the form $G=H\times K$ with $H$ non-amenable and $K$ infinite amenable and we deduce that any such group has uncountably many orbit inequivalent actions. | |
| dc.description | final version | |
| dc.identifier | https://arxiv.org/abs/math/0411164 | |
| dc.identifier | http://arxiv.org/abs/math/0411164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100932 | |
| dc.subject | Operator Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 46L55, 46L10, 46L40, 22D25, 22D40, 28D15 | |
| dc.title | A relative version of Connes' $χ(M)$ invariant and existence of orbit inequivalent actions | |
| dc.type | text |