Geometric construction of cluster algebras and cluster categories

Details Geometric construction of cluster algebras and cluster categories Geometric construction of cluster algebras and cluster categories

2008-04-25

arxiv.org/abs/0804.4065v1

Trends in Mathematics, R. Meyer, T. Schick, Y. Tschinkel (Eds.), Mathematisches Institut, Georg-August-Universit\"at G\"otting

Mathematics

Combinatorics

13 pages, 12 figures. This is an expanded version of a survey talk at the Courant-Colloquium Goettingen Trends in Mathematics,

Scientific paper

In this note we explain how to obtain cluster algebras from triangulations of
(punctured) discs following the approach of S. Fomin, M. Shapiro and D.
Thurston. Furthermore, we give a description of m-cluster categories via
diagonals (arcs) in (punctured) polygons and of m-cluster categories via powers
of translation quivers as given in joint work with R. Marsh.

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