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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.

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

Bernhard Keller, le 8 juin 2005.

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