  We introduce and study a class of Iwanaga-Gorenstein algebras defined via
quivers with relations associated with symmetrizable Cartan matrices. These
algebras generalize the path algebras of quivers associated with symmetric
Cartan matrices. We also define a corresponding class of generalized
preprojective algebras. Without any assumption on the ground field, we obtain
new representation-theoretic realizations of all finite root systems.
