FROM TRIANGULATED CATEGORIES TO CLUSTER ALGEBRAS II
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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