Softcover ISBN:  9780821836606 
Product Code:  CBMS/103 
List Price:  $47.00 
Individual Price:  $37.60 
eBook ISBN:  9781470424633 
Product Code:  CBMS/103.E 
List Price:  $44.00 
Individual Price:  $35.20 
Softcover ISBN:  9780821836606 
eBook: ISBN:  9781470424633 
Product Code:  CBMS/103.B 
List Price:  $91.00 $69.00 
Softcover ISBN:  9780821836606 
Product Code:  CBMS/103 
List Price:  $47.00 
Individual Price:  $37.60 
eBook ISBN:  9781470424633 
Product Code:  CBMS/103.E 
List Price:  $44.00 
Individual Price:  $35.20 
Softcover ISBN:  9780821836606 
eBook ISBN:  9781470424633 
Product Code:  CBMS/103.B 
List Price:  $91.00 $69.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 103; 2005; 113 ppMSC: Primary 46; Secondary 22
Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including nonabelian duality, noncommutative geometry, and the classification of simple \(C^*\)algebras.
The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of \(C^*\)algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising.
The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
To read a review published in the Gazette of the Australian Mathematical Society, click here .
ReadershipGraduate students and research mathematicians interested in graph theory and operator algebras.

Table of Contents

Chapters

1. Introduction

Chapter 1. Directed graphs and CuntzKrieger families

Chapter 2. Uniqueness theorems for graph algebras

Chapter 3. Proofs of the uniqueness theorems

Chapter 4. Simplicity and ideal structure

Chapter 5. Arbitrary graphs

Chapter 6. Applications to nonabelian duality

Chapter 7. $K$theory of graph algebras

Chapter 8. CuntzPimsner algebras

Chapter 9. Topological graphs

Chapter 10. Higherrank graphs

Appendix A. Background material


Additional Material

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Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including nonabelian duality, noncommutative geometry, and the classification of simple \(C^*\)algebras.
The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of \(C^*\)algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising.
The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
To read a review published in the Gazette of the Australian Mathematical Society, click here .
Graduate students and research mathematicians interested in graph theory and operator algebras.

Chapters

1. Introduction

Chapter 1. Directed graphs and CuntzKrieger families

Chapter 2. Uniqueness theorems for graph algebras

Chapter 3. Proofs of the uniqueness theorems

Chapter 4. Simplicity and ideal structure

Chapter 5. Arbitrary graphs

Chapter 6. Applications to nonabelian duality

Chapter 7. $K$theory of graph algebras

Chapter 8. CuntzPimsner algebras

Chapter 9. Topological graphs

Chapter 10. Higherrank graphs

Appendix A. Background material