Leavitt Path Algebras

Description

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. Front Matter ....Pages i-xiii The Basics of Leavitt Path Algebras: Motivations, Definitions and Examples (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 1-31 Two-Sided Ideals (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 33-102 Idempotents, and Finitely Generated Projective Modules (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 103-150 General Ring-Theoretic Results (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 151-184 Graph C∗-Algebras, and Their Relationship to Leavitt Path Algebras (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 185-217 K-Theory (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 219-257 Generalizations, Applications, and Current Lines of Research (Gene Abrams, Pere Ara, Mercedes Siles Molina)....Pages 259-273 Back Matter ....Pages 275-289