Leavitt Path Algebras

1. Front Matter

   Pages i-xiii

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2. The Basics of Leavitt Path Algebras: Motivations, Definitions and Examples

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 1-31

3. Two-Sided Ideals

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 33-102

4. Idempotents, and Finitely Generated Projective Modules

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 103-150

5. General Ring-Theoretic Results

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 151-184

6. Graph C ^∗-Algebras, and Their Relationship to Leavitt Path Algebras

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 185-217

7. K-Theory

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 219-257

8. Generalizations, Applications, and Current Lines of Research

   • Gene Abrams, Pere Ara, Mercedes Siles Molina

   Pages 259-273

9. Back Matter

   Pages 275-289

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This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume.

Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry.


Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible. 

• Leavitt path algebras
• graph C*-algebras
• ideal structure Leavitt path algebras
• structure of idempotents
• K-theory
• algebraic K-theory
• Leavitt path algebras applications
• Leavitt path algebras generalizations
• 16Sxx, 16D25, 16D40, 16D50, 16E20, 16E40
• 16E50, 16N60, 16P20, 16P40, 46L05

“With the diversity of their potential audience in mind, the authors aim to reach various groups of readers with a self-contained exposition written in a lively style. … Being the first comprehensive exposition on an area of active research and diverse applications, this book will likely be of interest to many groups of readers: those looking for an introduction to Leavitt path algebras; those interested in more in-depth details, open questions, or recent research trends …” (Lia Vaš, zbMATH 1393.16001, 2018)

• Department of Mathematics, University of Colorado, Colorado Springs, USA

  Gene Abrams

• Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

  Pere Ara

• Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain

  Mercedes Siles Molina

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