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Homological Methods, Representation Theory, and Cluster Algebras : Crm Short Courses - Ibrahim Assem

Homological Methods, Representation Theory, and Cluster Algebras

Crm Short Courses

By: Ibrahim Assem (Editor), Sonia Trepode (Editor)

Paperback Published: 11th May 2019
ISBN: 9783030090296
Number Of Pages: 236

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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 Math matiques Pures et Appliqu es) 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

ISBN: 9783030090296
ISBN-10: 3030090299
Series: Crm Short Courses
Audience: General
Format: Paperback
Language: English
Number Of Pages: 236
Published: 11th May 2019
Publisher: Springer
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.34

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