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.
Keywords.Quiver with relations Jacobian ideal potential mutation
Mathematics Subject Classification (2000).Primary 16G10 Secondary 16G20, 16S38
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