Classification of inductive limits of continuous trace C*-algebras: Classification of inductive limits of continuous trace C*-algebras - the case of simple separable C*-algebras - Couverture souple

Ivanescu, Cristian

 
9783838303253: Classification of inductive limits of continuous trace C*-algebras: Classification of inductive limits of continuous trace C*-algebras - the case of simple separable C*-algebras
Couverture souple
ISBN 10 : 3838303253 ISBN 13 : 9783838303253
Editeur : LAP LAMBERT Academic Publishing, 2009

Synopsis

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of simple C*-algebras which are inductive limits of continuous trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0,1]. In particular, a classification of simple stably AI algebras is obtained. Also, the range of the invariant is calculated. We start by approximating the building blocks appearing in a given inductive limit decomposition by certain special building blocks. The special building blocks are continuous trace C*-algebras with finite dimensional irreducible representations and such that the dimension of the representations, as a function on the interval, is a finite (lower semicontinuous) step function. It is then proved that these C*-algebras have finite presentations and stable relations. The advantage of having inductive limits of special subhomogeneous algebras is that we can prove the existence of certain gaps for the induced maps between the affine function spaces. These gaps are necessary to prove the Existence Theorem. Also the Uniqueness theorem is proved for these special building blocks.

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Présentation de l'éditeur

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of simple C*-algebras which are inductive limits of continuous trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0,1]. In particular, a classification of simple stably AI algebras is obtained. Also, the range of the invariant is calculated. We start by approximating the building blocks appearing in a given inductive limit decomposition by certain special building blocks. The special building blocks are continuous trace C*-algebras with finite dimensional irreducible representations and such that the dimension of the representations, as a function on the interval, is a finite (lower semicontinuous) step function. It is then proved that these C*-algebras have finite presentations and stable relations. The advantage of having inductive limits of special subhomogeneous algebras is that we can prove the existence of certain gaps for the induced maps between the affine function spaces. These gaps are necessary to prove the Existence Theorem. Also the Uniqueness theorem is proved for these special building blocks.

Biographie de l'auteur

Dr. Ivanescu defended his Ph.D. thesis in 2004 at University of Toronto. After defending his doctoral thesis he continued his research interests in C*-algebras and published research papers in various journals like Journal of Functional Analysis, Journal fur die reine und angewandte Mathematik.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2009
Langue
anglais
ISBN 10 
3838303253
ISBN 13 
9783838303253
Reliure
Broché
Nombre de pages
88
Coordonnées du fabricant
non disponible
Personne responsable
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