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arXiv · 1001.4360

The cluster character for cyclic quivers

Ming Ding·Fan Xu
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Abstract

We define an analogue of the Caldero-Chapoton map (\cite{CC}) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character (in the sense of \cite{Palu}) and satisfies some inductive formulas for the multiplication between the generalized cluster variables (the images of objects of the cluster category under the map). Moreover, we construct a $\mathbb{Z}$-basis for the algebras generated by all generalized cluster variables.

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Ming Ding, Fan Xu. 2010-01-25. The cluster character for cyclic quivers. https://arxiv.org/abs/1001.4360

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