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Quivers with relations for symmetrizable Cartan matrices I : Foundations (1410.1403v5)
Published 6 Oct 2014 in math.RT
Abstract: 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.
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