Cluster-Cyclic Quivers with three Vertices and the Markov Equation
Rings and Algebras
2011-11-09 v2 Representation Theory
Abstract
Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver it is thus desirable to decide if the cluster algebra defined by is acyclic. We call cluster-acyclic in this case, otherwise cluster-cyclic. In this note we classify the cluster-cyclic quivers with three vertices using a Diophantine equation studied by Markov.
Cite
@article{arxiv.math/0612213,
title = {Cluster-Cyclic Quivers with three Vertices and the Markov Equation},
author = {Andre Beineke and Thomas Brüstle and Lutz Hille},
journal= {arXiv preprint arXiv:math/0612213},
year = {2011}
}
Comments
11 pages, with an appendix by Otto Kerner