Quivers with potentials and their representations I: Mutations

• Harm Derksen ^[1] ; Jerzy Weyman ^[2] ; Andrei Zelevinsky ^[2]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  2. [2] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 1, 2008, págs. 59-119
• Idioma: inglés
• DOI: 10.1007/s00029-008-0057-9
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• Resumen

  • 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.