From triangulated categories to cluster algebras |
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Authors: | Philippe Caldero Bernhard Keller |
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Institution: | (1) Institut Camille Jordan, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France;(2) UFR de mathématiques, Université Denis Diderot – Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France |
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Abstract: | The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove
that a cluster algebra of finite type can be realized as a Hall algebra, called exceptional Hall algebra, of the cluster category. This realization
provides a natural basis for . We prove new results and formulate conjectures on ‘good basis’ properties, positivity, denominator theorems and toric degenerations. |
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Keywords: | |
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