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Quivers with potentials and their representations I: Mutations

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We study quivers with relations given by noncommutative 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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Correspondence to Harm Derksen.

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Derksen, H., Weyman, J. & Zelevinsky, A. Quivers with potentials and their representations I: Mutations. Sel. math., New ser. 14, 59–119 (2008).

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Mathematics Subject Classification (2000).