Semicanonical basis generators of the cluster algebra of type $A_1^{(1)}$
| dc.creator | Zelevinsky, Andrei | |
| dc.date | 2006-06-30 | |
| dc.date.accessioned | 2026-07-07T07:17:52Z | |
| dc.date.available | 2026-07-07T07:17:52Z | |
| dc.description | We study the cluster variables and "imaginary" elements of the semicanonical basis for the coefficient-free cluster algebra of affine type $A_1^{(1)}$. A closed formula for the Laurent expansions of these elements was obtained by P.Caldero and the author in math.RT/0604054. As a by-product, there was given a combinatorial interpretation of the Laurent polynomials in question, equivalent to the one obtained by G.Musiker and J.Propp in math.CO/0602408. The arguments in math.RT/0604054 used a geometric interpretation of the Laurent polynomials due to P.Caldero and F.Chapoton (math.RT/0410184). This note provides a quick, self-contained and completely elementary alternative proof of the same results. | |
| dc.description | 4 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0606775 | |
| dc.identifier | http://arxiv.org/abs/math/0606775 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114099 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 16S99 | |
| dc.title | Semicanonical basis generators of the cluster algebra of type $A_1^{(1)}$ | |
| dc.type | text |