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 for...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.展开更多
文摘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.
