Quivers with potentials and their representations I: Mutations

Details Quivers with potentials and their representations I: Mutations Quivers with potentials and their representations I: Mutations

2007-04-04

arxiv.org/abs/0704.0649v4

Mathematics

Rings and Algebras

58 pages; v.2: a typo fixed, references rearranged in the correct alphabetical order, an acknowledgment added; v.3: more typos

Scientific paper

We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This gives a far-reaching generalization of Bernstein-Gelfand-Ponomarev reflection functors. The motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras, cluster algebras.

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