Selecta Mathematica

, Volume 14, Issue 1, pp 59–119 | Cite as

Quivers with potentials and their representations I: Mutations

  • Harm DerksenEmail author
  • Jerzy Weyman
  • Andrei Zelevinsky


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.


Quiver with relations Jacobian ideal potential mutation 

Mathematics Subject Classification (2000).

Primary 16G10 Secondary 16G20, 16S38 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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