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Leavitt Path Algebras

  • Book
  • © 2017

Overview

Authors:
  1. Gene Abrams

    1. Department of Mathematics, University of Colorado, Colorado Springs, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Pere Ara

    1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

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    You can also search for this author in PubMed   Google Scholar

  3. Mercedes Siles Molina

    1. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain

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    You can also search for this author in PubMed   Google Scholar

  • The first book solely devoted to Leavitt path algebras
  • Provides a self-contained and easy-to-read introduction to the subject
  • Carefully explains the connection between graph C*-algebras and Leavitt path algebras
  • Presents fundamental results and new results alongside open problems

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2191)

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Table of contents (7 chapters)

  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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Keywords

About this book

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. 


Reviews

“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)

Authors and Affiliations

  • 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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