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

Cristian Ivanescu

ISBN 10: 3838303253 / ISBN 13: 9783838303253

Published by LAP LAMBERT Academic Publishing, 2009

About this Item

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 | Cristian Ivanescu | Taschenbuch | 88 S. | Englisch | 2009 | LAP LAMBERT Academic Publishing | EAN 9783838303253 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.

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Bibliographic Details

• Title: 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
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2009
• Language: English
• ISBN 10: 3838303253
• ISBN 13: 9783838303253
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 6D millimeters 220 millimeters width by 150 millimeters height by 6 millimeters depth
• Weight: 149 grams
• Seller catalogs:
  • Bücher

About this title

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.

About the Author

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.