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From triangulated categories to cluster algebras II

Philippe Caldero·Bernhard Keller
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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.

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Philippe Caldero, Bernhard Keller. 2006-04-12. From triangulated categories to cluster algebras II. https://arxiv.org/abs/math/0510251

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