• Corpus ID: 115167709

# Mutations for quivers with potentials: Oberwolfach talk, April 2007

@article{Zelevinsky2007MutationsFQ,
title={Mutations for quivers with potentials: Oberwolfach talk, April 2007},
author={Andrei Zelevinsky},
journal={arXiv: Rings and Algebras},
year={2007}
}
• A. Zelevinsky
• Published 6 June 2007
• Mathematics
• arXiv: Rings and Algebras
This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).

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## References

SHOWING 1-2 OF 2 REFERENCES

### Generalized associahedra via quiver representations

• Mathematics
• 2002
We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties

### Quivers with potentials and their representations I: Mutations

• Mathematics
• 2007
Abstract.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