Cluster characters II: A multiplication formula
Abstract
Let be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on which are satisfied for instance by cluster categories, by generalized cluster categories and by stable categories of modules over a preprojective algebra, we prove a multiplication formula for the cluster character associated with any cluster tilting object. This formula generalizes those obtained by Caldero-Keller for representation finite path algebras and by Xiao-Xu for finite-dimensional path algebras. It is analogous to a formula obtained by Geiss-Leclerc-Schr\"oer in the context of preprojective algebras.
Cite
@article{arxiv.0903.3281,
title = {Cluster characters II: A multiplication formula},
author = {Yann Palu},
journal= {arXiv preprint arXiv:0903.3281},
year = {2014}
}
Comments
v3: Updated references. Section on Fu--Keller's cluster character. v4: Some expository changes as suggested by the referee. To appear in Proceedings LMS