FROM TRIANGULATED CATEGORIES TO CLUSTER ALGEBRAS II

Philippe Caldero and Bernhard Keller

In the acyclic case, we etablish 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 positivity 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.

http://www.math.jussieu.fr/~keller/publ/ck2abs.html

Bernhard Keller, le 16 octobre 2005.
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