| Résume | It follows from a theorem of Keller and Reiten that a cluster category $C_Q$ can be realized as the stable category of certain subcategory $C_M$ of the module category of the corresponding preprojective algebra. We present explicitly a functor from $C_M$ to $C_Q= D^b(kQ)/$. Moreover, we show that the acyclic cluster algebra with coefficients which is categorified by $C_M$ is a polynomial ring which comes with a kind of dual PBW basis. |
