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Classification of Simple \(C\)*-algebras: Inductive Limits of Matrix Algebras over Trees
Liangqing Li, The Fields Institute, Toronto, ON, Canada
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Memoirs of the American Mathematical Society
1997; 123 pp; softcover
Volume: 127
ISBN-10: 0-8218-0596-7
ISBN-13: 978-0-8218-0596-1
List Price: US$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/127/605
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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

  • Introduction
  • Diagonalization, distinct spectrum and injectivity
  • Berg technique
  • Approximate divisibility
  • Uniqueness theorem
  • Existence theorem and classification
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