An approach to non simply laced cluster algebras
| dc.creator | Dupont, G. | |
| dc.date | 2005-12-01 | |
| dc.date | 2009-01-30 | |
| dc.date.accessioned | 2026-07-07T12:35:44Z | |
| dc.date.available | 2026-07-07T12:35:44Z | |
| dc.description | Let $Δ$ be an oriented valued graph equipped with a group of admissible automorphisms satisfying a certain stability condition. We prove that the (coefficient-free) cluster algebra $\mathcal A(Δ/G)$ associated to the valued quotient graph $Δ/G$ is a subalgebra of the quotient $π(\mathcal A(Δ))$ of the cluster algebra associated to $Δ$ by the action of $G$. When $Δ$ is a Dynkin diagram, we prove that $\mathcal A(Δ/G)$ and $π(\mathcal A(Δ))$ coincide. As an example of application, we prove that affine valued graphs are mutation-finite, giving an alternative proof to a result of Seven. | |
| dc.description | 36 pages. Minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0512043 | |
| dc.identifier | http://arxiv.org/abs/math/0512043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217862 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 22E99 | |
| dc.title | An approach to non simply laced cluster algebras | |
| dc.type | text |