Cluster characters for cyclic quivers
Cluster characters for cyclic quivers
摘要
We define an analogue of the Caldero-Chapoton map for the cluster category of finite-dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character and satisfies some inductive formulas for the multiplication between the generalized cluster variables （the images of objects of the cluster category under this map）. Moreover, we construct a Z-basis for the algebra generated by all generalized cluster variables.
We define an analogue of the Caldero-Chapoton map for the cluster category of finite-dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character and satisfies some inductive formulas for the multiplication between the generalized cluster variables （the images of objects of the cluster category under this map）. Moreover, we construct a Z-basis for the algebra generated by all generalized cluster variables.
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