Homological Methods, Representation Theory, and Cluster Algebras

Homological Methods, Representation Theory, and Cluster Algebras
Author :
Publisher : Springer
Total Pages : 231
Release :
ISBN-10 : 9783319745855
ISBN-13 : 3319745859
Rating : 4/5 (859 Downloads)

Book Synopsis Homological Methods, Representation Theory, and Cluster Algebras by : Ibrahim Assem

Download or read book Homological Methods, Representation Theory, and Cluster Algebras written by Ibrahim Assem and published by Springer. This book was released on 2018-04-18 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Homological Methods, Representation Theory, and Cluster Algebras Related Books

Homological Methods, Representation Theory, and Cluster Algebras
Language: en
Pages: 231
Authors: Ibrahim Assem
Categories: Mathematics
Type: BOOK - Published: 2018-04-18 - Publisher: Springer

GET EBOOK

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theo
Quiver Representations
Language: en
Pages: 233
Authors: Ralf Schiffler
Categories: Mathematics
Type: BOOK - Published: 2014-09-04 - Publisher: Springer

GET EBOOK

This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part
Lecture Notes on Cluster Algebras
Language: en
Pages: 132
Authors: Robert J. Marsh
Categories: Mathematics
Type: BOOK - Published: 2013 - Publisher: Erich Schmidt Verlag GmbH & Co. KG

GET EBOOK

Cluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical
Advances in Representation Theory of Algebras
Language: en
Pages: 257
Authors: Ibrahim Assem
Categories: Education
Type: BOOK - Published: 2021-01-06 - Publisher: American Mathematical Soc.

GET EBOOK

The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Au
Modern Trends in Algebra and Representation Theory
Language: en
Pages: 408
Authors: David Jordan
Categories: Mathematics
Type: BOOK - Published: 2023-07-31 - Publisher: Cambridge University Press

GET EBOOK

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of repr