Quivers with potentials and their representations I: Mutations
Rings and Algebras
2008-04-21 v4 Representation Theory
Abstract
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.
Cite
@article{arxiv.0704.0649,
title = {Quivers with potentials and their representations I: Mutations},
author = {Harm Derksen and Jerzy Weyman and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:0704.0649},
year = {2008}
}
Comments
58 pages; v.2: a typo fixed, references rearranged in the correct alphabetical order, an acknowledgment added; v.3: more typos fixed, minor editorial improvements; v.4: minor editorial changes, final version to appear in Selecta Math