English

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.

Keywords

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

R2 v1 2026-07-22T17:20:11.265Z