The generator problem for Z-stable C*-algebras
Thiel, Hannes
Winter, Wilhelm
Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2011
Description: 18 p.
Abstract: The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.
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: Centre de Recerca Matemàtica: Prepublicacions del Centre de Recerca Matemàtica
Series: Prepublicacions del Centre de Recerca Matemàtica ; 1079
Document: article ; submittedVersion
Subject: C*-àlgebres ; Grups, Teoria de -- Generadors ; Estabilitat

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18 p, 296.7 KB

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Research literature > Preprints

 Record created 2018-10-23, last modified 2018-12-22

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