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. 
View PDF on arXiv
7 Citations
Background Citations
2

7 Citations

Calabi-Yau algebras and superpotentials
We prove that complete $$d$$d-Calabi-Yau algebras in the sense of Ginzburg are derived from superpotentials.
APR Tilting Modules and Graded Quivers with Potential
We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and…
Non-commutative crepant resolutions, an overview
Non-commutative crepant resolutions (NCCRs) are non-commutative analogues of the usual crepant resolutions that appear in algebraic geometry. In this paper we survey some results around NCCRs.
Finite-dimensional algebras are (m>2)-Calabi-Yau-tilted
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any…
On generalized cluster categories
Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the construction of a…
Higher APR tilting preserves $n$-representation infiniteness
On Maximal Green Sequences
Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maximal green sequences…

References

SHOWING 1-10 OF 20 REFERENCES
Quivers with potentials and their representations I: Mutations
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…
Derived equivalences from mutations of quivers with potential
Calabi-Yau algebras and superpotentials
We prove that complete $$d$$d-Calabi-Yau algebras in the sense of Ginzburg are derived from superpotentials.
Graded Calabi Yau algebras of dimension 3
The A∞ Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus
Gorenstein Isolated Quotient Singularities of Odd Prime Dimension are Cyclic
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,…
Helices on del Pezzo surfaces and tilting Calabi-Yau algebras
Generators and representability of functors in commutative and noncommutative geometry
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
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…
Superpotentials and higher order derivations
...
...