From triangulated categories to cluster algebras

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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.
31 pages, typos corrected

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Representation Theory, Rings and Algebras, 16G20; 18E30

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http://salesiana.dossiersoluciones.com/handle/123456789/75383

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506018
 http://arxiv.org/abs/math/0506018

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arXiv