To cite this record:
Recovering the Elliott invariant from the Cuntz semigroup
Antoine Riolobos, Ramon
Dadarlat, Màrius
Perera Domènech, Francesc
Santiago, Luís
Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2011
Description: 16 p.
Abstract: 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.
Rights: L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: Creative Commons
Language: Anglès.
Series: Prepublicacions del Centre de Recerca Matemàtica
Series: Prepublicacions del Centre de Recerca Matemàtica ; 1043
Document: preprint
Subject: Àlgebres d'operadors

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16 p, 230.7 KB

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Research literature > Preprints

 Record created 2012-03-15, last modified 2016-06-11

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