88585 driver oai:ddd.uab.cat:88585 hdl_2072_1177 oai:www.recercat.cat:2072/182298 eng 517 Antoine Riolobos, Ramon Recovering the Elliott invariant from the Cuntz semigroup Centre de Recerca Matemàtica 2011 16 p. Let A be a simple, separable C*-algebra of stable rank one. We prove that the Cuntz semigroup of C (T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C (T, A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor defined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent. info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Àlgebres d'operadors info:eu-repo/semantics/preprint Dadarlat, Màrius Perera Domènech, Francesc Santiago, Luís Centre de Recerca Matemàtica Prepublicacions del Centre de Recerca Matemàtica ; 1043 16 236263 http://ddd.uab.cat/pub/prepub/2011/hdl_2072_182298/Pr1043.pdf Adreça alternativa http://hdl.handle.net/2072/182298 PREPUB UAB file 0 MD5 d9ddd706f64901c6408f2a9263e3f7d3 236263 PDF 1.4 filepath pub/prepub/2011/hdl_2072_182298/Pr1043.pdf disk