From triangulated categories to cluster algebras II
Representation Theory
2007-05-23 v2 Rings and Algebras
Abstract
In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator theorem, and some conjectures on properties of the mutation graph. As in the previous article, the proofs rely on the Calabi-Yau property of the cluster category.
Cite
@article{arxiv.math/0510251,
title = {From triangulated categories to cluster algebras II},
author = {Philippe Caldero and Bernhard Keller},
journal= {arXiv preprint arXiv:math/0510251},
year = {2007}
}
Comments
23 pages. The proofs rely on a weaker version of positivity