Cluster algebras, quiver representations and triangulated categories. (English) Zbl 1215.16012

Keller, Bernhard

Holm, Thorsten (ed.) et al., Triangulated categories. Based on a workshop, Leeds, UK, August 2006. Cambridge: Cambridge University Press (ISBN 978-0-521-74431-7/pbk). London Mathematical Society Lecture Note Series 375, 76-160 (2010).

Summary: This is an introduction to some aspects of Fomin-Zelevinsky’s cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer schools held in 2006 (Bavaria) and 2008 (Jerusalem). In addition to by now classical material, we present the outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams (details will appear elsewhere) and recent results on the interpretation of mutations as derived equivalences.
For the entire collection see [Zbl 1195.18001].

MSC:

16G20	Representations of quivers and partially ordered sets
13F60	Cluster algebras
18E30	Derived categories, triangulated categories (MSC2010)

Keywords:

cluster algebras; representations of quivers; Calabi-Yau triangulated categories; pairs of Dynkin diagrams; derived equivalences

Software:

quivermutation