Denominators in cluster algebras of affine type
Representation Theory
2020-12-21 v2 Rings and Algebras
Abstract
The Fomin-Zelevinsky Laurent phenomenon states that every cluster variable in a cluster algebra can be expressed as a Laurent polynomial in the variables lying in an arbitrary initial cluster. We give representation-theoretic formulas for the denominators of cluster variables in cluster algebras of affine type. The formulas are in terms of the dimensions of spaces of homomorphisms in the corresponding cluster category, and hold for any choice of initial cluster.
Keywords
Cite
@article{arxiv.0805.0439,
title = {Denominators in cluster algebras of affine type},
author = {Aslak Bakke Buan and Bethany Marsh},
journal= {arXiv preprint arXiv:0805.0439},
year = {2020}
}
Comments
22 pages, no figures. Correction to Defn 1.2. Minor corrections