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Quivers with relations arising from clusters (A_n case)

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arxiv math/0401316 v1 pith:INKMZLP2 submitted 2004-01-23 math.RT math.RA

Philippe Caldero , Frederic Chapoton , Ralf Schiffler This is my paper · ORCID
classification math.RTmath.RA
keywords clusterfominrealizationzelevinskyabelianalgebraalgebraicalgebras
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Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type A_n. We associate to each cluster C of U an abelian category Cat_C such that the indecomposable objects of Cat_C are in natural correspondence with the cluster variables of U which are not in C. We give an algebraic realization and a geometric realization of Cat_C. Then, we generalize the ``denominator Theorem'' of Fomin and Zelevinsky to any cluster.

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  1. Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

    math.RT 2025-08 unverdicted novelty 7.0 of 10

    The paper constructs infinite discrete Nakayama representations via persistence theory and stabilizes them into negative Calabi-Yau versions of Igusa-Todorov discrete cluster categories of type A, with geometric model...

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