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Cluster algebras and categorification - Lecture 1

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Post-edited
Authors : Amiot, Claire (Author of the conference)
CIRM (Publisher )

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triangulations flip of triangulation cluster algebra associated with surface example of cluster algebra of type $A_2$ Somos sequence definition of cluster algebra general definition of cluster algebra
Abstract : In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of cluster algebras in this context. All the notions will be illustrated by examples.

Keywords : cluster category; cluster-tilting theory

MSC Codes :
16G20 - Representations of quivers and partially ordered sets
 18E30 - Derived categories, triangulated categories
 13F60 - Cluster algebras
 16E35 - Derived categories in associative algebra
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 13/02/2018
    Conference Date : 06/02/2018
    Subseries : Research School
    arXiv category : Representation Theory ; Rings and Algebras ; Combinatorics
    Mathematical Area(s) : Algebra ; Combinatorics
    Format : MP4 (.mp4) - HD
    Video Time : 01:03:16
    Targeted Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2018-02-06_Amiot_Part1.mp4
Information on the Event

Event Title : Winter Braids VIII
Event Organizers : Audoux, Benjamin ; Bellingeri, Paolo ; Florens, Vincent ; Meilhan, Jean-Baptiste ; Wagner, Emmanuel
Dates : 05/02/2018 - 09/02/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1892.html

Citation Data

DOI : 10.24350/CIRM.V.19346703
Cite this video as: Amiot, Claire (2018). Cluster algebras and categorification - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19346703
URI : http://dx.doi.org/10.24350/CIRM.V.19346703

See Also

Bibliography

  • Fomin, S., Shapiro, M., & Thurston, D. (2008). Cluster algebras and triangulated surfaces. I: Cluster complexes. Acta Mathematica, 201(1), 83-146 - https://doi.org/10.1007/s11511-008-0030-7

  • Fomin, S., & Zelevinsky, A. (2002). Cluster algebras. I: Foundations. Journal of the American Mathematical Society, 15(2), 497-529 - https://doi.org/10.1090/S0894-0347-01-00385-X

  • Keller, B. (2010). Cluster algebras, quiver representations and triangulated categories. In T. Holm, P. Jorgensen, & R. Rouquier (Eds.), Triangulated categories (pp. 76-160). Cambridge: Cambridge University Press - http://www.arxiv.org/abs/0807.1960


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