Let $Q$ be a finite quiver without oriented cycles. In https://arxiv.org/abs/0807.1960 , Keller defines the dg cluster category $C_Q$ of $Q$. When is $C_Q$ smooth proper dg-category? If $Q$ is a Dynkin quiver, then $C_Q$ might be smooth proper.
Let $Q$ be a finite quiver without oriented cycles. In https://arxiv.org/abs/0807.1960 , Keller defines the dg cluster category $C_Q$ of $Q$. When is $C_Q$ smooth proper dg-category? If $Q$ is a Dynkin quiver, then $C_Q$ might be smooth proper.