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Mutations for quivers with potentials and their representations
Andrei Zelevinsky (Northeastern University)
March 23, 2007

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Abstract:

This lecture is based on joint work in progress with H.Derksen and
J.Weyman. We obtain a far-reaching generalization of classical
Bernstein-Gelfand-Ponomarev reflection functors playing a
fundamental role in the theory of quiver representations. These
functors are defined only at a source or a sink of the quiver in
question. We introduce a class of quivers with relations of a
special kind given by non-commutative analogs of Jacobian ideals in
the path algebra. We then define the mutations at arbitrary vertices
for these quivers and their representations. If the vertex in
question is a source or a sink, our mutations specialize to
reflection functors. The motivations for this work come from several
sources: superpotentials in physics, Calabi-Yau algebras, cluster
algebras. We will keep the exposition elementary, with all necessary
background explained from scratch.

 

Lecture Notes (by D. Ben-Zvi): pages 1

 

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