FROM TRIANGULATED CATEGORIES TO CLUSTER ALGEBRAS
The cluster category is a triangulated category introduced for its
combinatorial similarities with cluster algebras. We prove that a
cluster algebra A of finite type can be realized as a Hall
algebra, called the exceptional Hall algebra, of the cluster
category. This realization provides a natural basis for A. We prove
new results and formulate conjectures on 'good basis' properties, positivity,
denominator theorems and toric degenerations.
Bernhard Keller, le 8 juin 2005.