Semicanonical basis generators of the cluster algebra of type $A_1^{(1)}$
Rings and Algebras
2007-05-23 v1 Combinatorics
Abstract
We study the cluster variables and "imaginary" elements of the semicanonical basis for the coefficient-free cluster algebra of affine type . 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.
Keywords
Cite
@article{arxiv.math/0606775,
title = {Semicanonical basis generators of the cluster algebra of type $A_1^{(1)}$},
author = {Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0606775},
year = {2007}
}
Comments
4 pages, no figures