Advertisement

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 1-31
  3. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 33-102
  4. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 103-150
  5. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 151-184
  6. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 185-217
  7. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 219-257
  8. Gene Abrams, Pere Ara, Mercedes Siles Molina
    Pages 259-273
  9. Back Matter
    Pages 275-289

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Gene Abrams
    • 1
  • Pere Ara
    • 2
  • Mercedes Siles Molina
    • 3
  1. 1.Department of MathematicsUniversity of ColoradoColorado SpringsUSA
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  3. 3.Departamento de Álgebra, Geometría y TopologíaUniversidad de MálagaMálagaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-7344-1
  • Copyright Information Springer-Verlag London Ltd. 2017
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-7343-4
  • Online ISBN 978-1-4471-7344-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site