From triangulated categories to cluster algebras
Representation Theory
2007-05-23 v2 Rings and Algebras
Abstract
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of the cluster category. This realization provides a natural basis for A. We prove new results and formulate conjectures on `good basis' properties, positivity, denominator theorems and toric degenerations.
Cite
@article{arxiv.math/0506018,
title = {From triangulated categories to cluster algebras},
author = {Philippe Caldero and Bernhard Keller},
journal= {arXiv preprint arXiv:math/0506018},
year = {2007}
}
Comments
31 pages, typos corrected