Quivers with relations for symmetrizable Cartan matrices I : Foundations
  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. 
Christof Geiss, Bernard Leclerc, Jan Schr\"oer
math.RT