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Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees
 
Liangqing Li The Fields Institute, Toronto, ON, Canada
Front Cover for Classification of Simple C*-algebras: Inductive Limits of Matrix Algebras over Trees
Available Formats:
Electronic ISBN: 978-1-4704-0190-0
Product Code: MEMO/127/605.E
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $28.80
Front Cover for Classification of Simple C*-algebras: Inductive Limits of Matrix Algebras over Trees
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  • Front Cover for Classification of Simple C*-algebras: Inductive Limits of Matrix Algebras over Trees
  • Back Cover for Classification of Simple C*-algebras: Inductive Limits of Matrix Algebras over Trees
Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees
Liangqing Li The Fields Institute, Toronto, ON, Canada
Available Formats:
Electronic ISBN:  978-1-4704-0190-0
Product Code:  MEMO/127/605.E
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $28.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1271997; 123 pp
    MSC: Primary 46; Secondary 19; 47;

    In this book, it is shown that the simple unital \(C^*\)-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over \(C(X_i)\), where \(X_i\) are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of \(X_i = [0,1]\). The added generality is useful in the classification of more general inductive limit \(C^*\)-algebras.

    Readership

    Graduate students and research mathematicians interested in the classification problem of \(C^*\)-algebras or the general theory of \(C^*\)-algebras.

  • Table of Contents
     
     
    • Chapters
    • 1 Introduction
    • 2 Diagonalization, distinct spectrum and injectivity
    • 3 Berg technique
    • 4 Approximate divisibility
    • 5 Uniqueness theorem
    • 6 Existence theorem and classification
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Volume: 1271997; 123 pp
MSC: Primary 46; Secondary 19; 47;

In this book, it is shown that the simple unital \(C^*\)-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over \(C(X_i)\), where \(X_i\) are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of \(X_i = [0,1]\). The added generality is useful in the classification of more general inductive limit \(C^*\)-algebras.

Readership

Graduate students and research mathematicians interested in the classification problem of \(C^*\)-algebras or the general theory of \(C^*\)-algebras.

  • Chapters
  • 1 Introduction
  • 2 Diagonalization, distinct spectrum and injectivity
  • 3 Berg technique
  • 4 Approximate divisibility
  • 5 Uniqueness theorem
  • 6 Existence theorem and classification
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