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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
123 pp
List Price: $48.00 MAA Member Price:$43.20
AMS Member Price: $28.80 Click above image for expanded view Classification of Simple$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 123 pp  List Price:$48.00 MAA Member Price: $43.20 AMS Member Price:$28.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1271997
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.

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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Volume: 1271997
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.

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