Some new examples of non-degenerate quiver potentials
@article{Volcsey2010SomeNE, title={Some new examples of non-degenerate quiver potentials}, author={Louis de Thanhoffer de Volcsey and Michel van den Bergh}, journal={arXiv: Combinatorics}, year={2010} }
We prove a technical result which allows us to establish the non-degeneracy of potentials on quivers in some previously unknown or non-obvious cases.
Our result applies to certain McKay quivers and also to potentials derived from geometric helices on Del Pezzo surfaces.
6 Citations
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References
SHOWING 1-10 OF 20 REFERENCES
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…
Calabi-Yau algebras and superpotentials
- Mathematics
- 2010
We prove that complete $$d$$d-Calabi-Yau algebras in the sense of Ginzburg are derived from superpotentials.
Gorenstein Isolated Quotient Singularities of Odd Prime Dimension are Cyclic
- Mathematics
- 2009
In this article, we shall prove that Gorenstein isolated quotient singularities of odd prime dimension are cyclic. In the case where the dimension is bigger than 1 and is not an odd prime number,…
Generators and representability of functors in commutative and noncommutative geometry
- Mathematics
- 2002
We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is…
HOMOLOGICAL PROPERTIES OF ASSOCIATIVE ALGEBRAS: THE METHOD OF HELICES
- Mathematics
- 1994
Homological properties of associative algebras arising in the theory of helices are studied. A class of noncommutative algebras is introduced in which it is natural (from the viewpoint of the theory…