From triangulated categories to cluster algebras

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From triangulated categories to cluster algebras

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by Philippe Caldero , Bernhard Keller

Citations:

172 - 20 self

BibTeX

@MISC{Caldero_fromtriangulated,
    author = {Philippe Caldero and Bernhard Keller},
    title = {From triangulated categories to cluster algebras},
    year = {}
}

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Abstract

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. 1.

Keyphrases

cluster category associated cluster algebra denominator theorem previous article mutation graph calabi-yau property multiplicativity theorem one-to-one correspondence acyclic case cluster algebra

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