On cluster algebras with coefficients and 2-Calabi-Yau categories
Representation Theory
2009-01-09 v4 Rings and Algebras
Abstract
Building on work by Geiss-Leclerc-Schroer and by Buan-Iyama-Reiten-Scott we investigate the link between certain cluster algebras with coefficients and suitable 2-Calabi-Yau categories. These include the cluster-categories associated with acyclic quivers and certain Frobenius subcategories of module categories over preprojective algebras. Our motivation comes from the conjectures formulated by Fomin and Zelevinsky in `Cluster algebras IV: Coefficients'. We provide new evidence for Conjectures 5.4, 6.10, 7.2, 7.10 and 7.12 and show by an example that the statement of Conjecture 7.17 does not always hold.
Cite
@article{arxiv.0710.3152,
title = {On cluster algebras with coefficients and 2-Calabi-Yau categories},
author = {Changjian Fu and Bernhard Keller},
journal= {arXiv preprint arXiv:0710.3152},
year = {2009}
}
Comments
35 pages, section 2 added, readability improved, references updated, to appear in Trans. AMS