CRM Short Courses

Homological Methods, Representation Theory, and Cluster Algebras

Editors: Assem, Ibrahim, Trepode, Sonia (Eds.)

  • Underscores cluster algebras—one of the most important highlights of today's mathematical landscape
  • Addressed to graduate students, young researchers, and research mathematicians
  • Assumes minimal previous knowledge from readers while still taking them deeply into theory
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eBook $54.99
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  • ISBN 978-3-319-74585-5
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Hardcover $69.99
price for USA in USD
  • ISBN 978-3-319-74584-8
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About this Textbook

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.


The courses held were:
  • Advanced homological algebra
  • Introduction to the representation theory of algebras
  • Auslander-Reiten theory for algebras of infinite representation type
  • Cluster algebras arising from surfaces
  • Cluster tilted algebras
  • Cluster characters
  • Introduction to K-theory
  • Brauer graph algebras and applications to cluster algebras

About the authors

Ibrahim Assem is professor of mathematics at the University of Sherbrooke. Professor Assem’s research interest is in representation theory. He is a member of the Research Group on Algebra Representation Theory from the combined institutions: University of Sherbrooke and Bishop’s University.

Sonia Trepode is professor of mathematics at the Universidad Nacional de Mar del Plata, Argentina.

Table of contents (6 chapters)

  • Introduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach

    Platzeck, María Inés

    Pages 1-20

  • Auslander–Reiten Theory for Finite-Dimensional Algebras

    Malicki, Piotr

    Pages 21-63

  • Cluster Algebras from Surfaces

    Schiffler, Ralf

    Pages 65-99

  • Cluster Characters

    Plamondon, Pierre-Guy

    Pages 101-125

  • A Course on Cluster Tilted Algebras

    Assem, Ibrahim

    Pages 127-176

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-74585-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-319-74584-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Homological Methods, Representation Theory, and Cluster Algebras
Editors
  • Ibrahim Assem
  • Sonia Trepode
Series Title
CRM Short Courses
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-74585-5
DOI
10.1007/978-3-319-74585-5
Hardcover ISBN
978-3-319-74584-8
Series ISSN
2522-5200
Edition Number
1
Number of Pages
XI, 223
Number of Illustrations and Tables
41 b/w illustrations
Topics