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From the Basic Homotopy Lemma to the Classification of $C^*$-algebras
 
Huaxin Lin East China Normal University, Shanghai, China and University of Oregon, Eugene, OR
A co-publication of the AMS and CBMS
Front Cover for From the Basic Homotopy Lemma to the Classification of C^*-algebras
Available Formats:
Softcover ISBN: 978-1-4704-3490-8
Product Code: CBMS/124
240 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Electronic ISBN: 978-1-4704-4192-0
Product Code: CBMS/124.E
240 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Front Cover for From the Basic Homotopy Lemma to the Classification of C^*-algebras
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  • Front Cover for From the Basic Homotopy Lemma to the Classification of C^*-algebras
  • Back Cover for From the Basic Homotopy Lemma to the Classification of C^*-algebras
From the Basic Homotopy Lemma to the Classification of $C^*$-algebras
Huaxin Lin East China Normal University, Shanghai, China and University of Oregon, Eugene, OR
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN:  978-1-4704-3490-8
Product Code:  CBMS/124
240 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Electronic ISBN:  978-1-4704-4192-0
Product Code:  CBMS/124.E
240 pp 
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1242017
    MSC: Primary 46;

    This book examines some recent developments in the theory of \(C^*\)-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable \(C^*\)-algebras, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, \(KK\)-theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.

    A co-publication of the AMS and CBMS.

    Readership

    Graduate students and researchers interested in C*-algebras.

  • Table of Contents
     
     
    • Chapters
    • An overview of the Elliott program
    • An introduction to the Basic Homotopy Lemma
    • Maps to finite dimensional $C^*$-algebras
    • Stable homotopy lemmas
    • The Basic Homotopy Lemma, finite dimensional cases
    • $C^*$-algebras of generalized tracial rank one
    • More Basic Homotopy Lemmas
    • Asymptotic unitary equivalence
    • Classification of simple $C^*$-algebras of finite rank
  • Request Review Copy
Volume: 1242017
MSC: Primary 46;

This book examines some recent developments in the theory of \(C^*\)-algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable \(C^*\)-algebras, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, \(KK\)-theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.

A co-publication of the AMS and CBMS.

Readership

Graduate students and researchers interested in C*-algebras.

  • Chapters
  • An overview of the Elliott program
  • An introduction to the Basic Homotopy Lemma
  • Maps to finite dimensional $C^*$-algebras
  • Stable homotopy lemmas
  • The Basic Homotopy Lemma, finite dimensional cases
  • $C^*$-algebras of generalized tracial rank one
  • More Basic Homotopy Lemmas
  • Asymptotic unitary equivalence
  • Classification of simple $C^*$-algebras of finite rank
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