The preprojective algebra of a module $M$ over a finite dimensional algebra $A$ is defined as $P_M:= \bigoplus\limits_{n=0}^{\infty}{Hom_A(M, \tau^{-n}(M))}$ with the canonical multiplication.

Question 1: Is there an easy way to obtain quiver and relations of $P_M$ in case it is finite dimensional? Are explicit quiver and relations known when $M=A$ and $A$ is an acyclic Nakayama algebra?

Question 2: Can $P_M$ be obtained in qpa in some way in case it is finite dimensional, at least in some special cases like Nakayama algebras?