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Leavitt Path Algebras: Lecture Notes in Mathematics, cartea 2191

Autor Gene Abrams, Pere Ara, Mercedes Siles Molina
en Limba Engleză Paperback – 30 noi 2017
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. 

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Specificații

ISBN-13: 9781447173434
ISBN-10: 1447173430
Pagini: 200
Ilustrații: XIII, 289 p.
Dimensiuni: 155 x 235 x 29 mm
Greutate: 0.43 kg
Ediția:1st ed. 2017
Editura: SPRINGER LONDON
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:London, United Kingdom

Cuprins

1 The basics of Leavitt path algebras: motivations, definitions and examples.- 2 Two-sided ideals.- 3 Idempotents, and finitely generated projective modules.- 4 General ring-theoretic results.- 5 Graph C*-algebras, and their relationship to Leavitt path algebras.- 6 K-theory.- 7 Generalizations, applications, and current lines of research.- References.- Index.

Recenzii

“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)

Textul de pe ultima copertă

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.

Caracteristici

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