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. For these two classes of
algebras we obtain generalizations of classical results of Gabriel, Dlab–Ringel, and Gelfand–
Ponomarev. In particular, we obtain new representation theoretic realizations of all finite root …

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.