A relative version of Connes' $χ(M)$ invariant and existence of orbit inequivalent actions

dc.creatorIoana, Adrian
dc.date2004-11-08
dc.date2006-02-14
dc.date.accessioned2026-07-07T06:38:59Z
dc.date.available2026-07-07T06:38:59Z
dc.descriptionWe 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.descriptionfinal version
dc.identifierhttps://arxiv.org/abs/math/0411164
dc.identifierhttp://arxiv.org/abs/math/0411164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100932
dc.subjectOperator Algebras
dc.subjectGroup Theory
dc.subject46L55, 46L10, 46L40, 22D25, 22D40, 28D15
dc.titleA relative version of Connes' $χ(M)$ invariant and existence of orbit inequivalent actions
dc.typetext

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