A module-theoretic interpretation of Schiffler's expansion formula
Representation Theory
2011-05-31 v1
Abstract
We give a module-theoretic interpretation of Schiffler's expansion formula which is defined combinatorially in terms of complete (T,r)-paths in order to get the expansion of the cluster variables in the cluster algebra of a marked surface (S,M). Based on the geometric description of the indecomposable objects of the cluster category of the marked surface (S,M), we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined by Palu.
Keywords
Cite
@article{arxiv.1105.5673,
title = {A module-theoretic interpretation of Schiffler's expansion formula},
author = {Thomas Brüstle and Jie Zhang},
journal= {arXiv preprint arXiv:1105.5673},
year = {2011}
}