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H 2 Cluster algebras and categorification - Lecture 1

Auteurs : Amiot, Claire (Auteur de la Conférence)
CIRM (Editeur )

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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

Résumé : 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

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

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 13/02/2018
    Date de captation : 06/02/2018
    Collection : Research School ; Algebra ; Combinatorics
    Format : MP4 (.mp4) - HD
    Durée : 01:03:16
    Domaine : Algebra ; Combinatorics
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-02-06_Amiot_Part1.mp4

Informations sur la rencontre

Nom de la rencontre : Winter Braids VIII
Organisateurs de la rencontre : Audoux, Benjamin ; Bellingeri, Paolo ; Florens, Vincent ; Meilhan, Jean-Baptiste ; Wagner, Emmanuel
Dates : 05/02/2018 - 09/02/2018
Année de la rencontre : 2018
URL Congrès : 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

Voir aussi

Bibliographie

  • 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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