×

Homological methods, representation theory, and cluster algebras. Based on six mini-courses, CIMPA, Mar del Plata, Argentina, March 7–18, 2016. (English) Zbl 1395.16001

CRM Short Courses. Cham: Springer; Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-3-319-74584-8/hbk; 978-3-319-74585-5/ebook). xi, 223 p. (2018).

Show indexed articles as search result.

Publisher’s description: 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:
\(\bullet\)
Advanced homological algebra
\(\bullet\)
Introduction to the representation theory of algebras
\(\bullet\)
Auslander-Reiten theory for algebras of infinite representation type
\(\bullet\)
Cluster algebras arising from surfaces
\(\bullet\)
Cluster tilted algebras
\(\bullet\)
Cluster characters
\(\bullet\)
Introduction to K-theory
\(\bullet\)
Brauer graph algebras and applications to cluster algebras

The articles of this volume will be reviewed individually.
Indexed articles:
Platzeck, María Inés, Introduction to the representation theory of finite-dimensional algebras: the functorial approach, 1-20 [Zbl 1416.16013]
Malicki, Piotr, Auslander-Reiten theory for finite-dimensional algebras, 21-63 [Zbl 1426.16012]
Schiffler, Ralf, Cluster algebras from surfaces. Lecture notes for the CIMPA School Mar del Plata, March 2016, 65-99 [Zbl 1419.13044]
Plamondon, Pierre-Guy, Cluster characters, 101-125 [Zbl 1419.13043]
Assem, Ibrahim, A course on cluster tilted algebras, 127-176 [Zbl 1420.13052]
Schroll, Sibylle, Brauer graph algebras. A survey on Brauer graph algebras, associated gentle algebras and their connections to cluster theory, 177-223 [Zbl 1444.16023]

MSC:

16-06 Proceedings, conferences, collections, etc. pertaining to associative rings and algebras
16Gxx Representation theory of associative rings and algebras
16Exx Homological methods in associative algebras
00B25 Proceedings of conferences of miscellaneous specific interest
PDFBibTeX XMLCite
Full Text: DOI