Quivers with relations for symmetrizable Cartan matrices I: Foundations

By C. Geiss, Bernard Leclerc, J. Schröer. 2014

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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 systems without any assumption on the ground field.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d8bbdcd68298978cde9eff583d4b3cfafd386735