Denominator vectors and dimension vectors from triangulated surfaces
Combinatorics
2024-08-28 v2 Representation Theory
Abstract
In a categorification of skew-symmetric cluster algebras, each cluster variable corresponds with an indecomposable module over the associated Jacobian algebra. Buan, Marsh and Reiten studied when the denominator vector of each cluster variable in an acyclic cluster algebra coincides with the dimension vector of the corresponding module. In this paper, we give analogues of their results for cluster algebras from triangulated surfaces by comparing two kinds of intersection numbers of tagged arcs.
Keywords
Cite
@article{arxiv.2305.08097,
title = {Denominator vectors and dimension vectors from triangulated surfaces},
author = {Toshiya Yurikusa},
journal= {arXiv preprint arXiv:2305.08097},
year = {2024}
}
Comments
20 pages, v2: minor corrections