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Homological Methods, Representation Theory, and Cluster Algebras

  • Ibrahim Assem
  • Sonia Trepode

Part of the CRM Short Courses book series (CRMSC)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ralf Schiffler
    Pages 65-99
  3. Pierre-Guy Plamondon
    Pages 101-125
  4. Ibrahim Assem
    Pages 127-176
  5. Sibylle Schroll
    Pages 177-223

About this book

Introduction

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.

The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.

Keywords

Brauer graph algebras Auslander-Reiten translation cluster algebras K-theory Quillen's Q-construction finite-dimensional algebras cluster characters cluster tilted algebras Auslander-Reiten representation theory homological algebras cluster algebras textbook

Editors and affiliations

  • Ibrahim Assem
    • 1
  • Sonia Trepode
    • 2
  1. 1.Département de MathématiquesUniversité de SherbrookeSherbrookeCanada
  2. 2.Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de Mar del PlataMar del PlataArgentina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74585-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74584-8
  • Online ISBN 978-3-319-74585-5
  • Series Print ISSN 2522-5200
  • Series Online ISSN 2522-5219
  • Buy this book on publisher's site