Quivers with potentials and their representations I: Mutations

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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.
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

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Rings and Algebras, Representation Theory, 16G10 (Primary); 16G20, 16S38 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/159091

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.0649
 http://arxiv.org/abs/0704.0649

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arXiv