Graded Calabi Yau Algebras of dimension 3

Details Graded Calabi Yau Algebras of dimension 3 Graded Calabi Yau Algebras of dimension 3

2006-03-23

arxiv.org/abs/math/0603558v1

Mathematics

Rings and Algebras

With an appendix by Michel Van den Bergh

Scientific paper

In this paper we prove that Graded Calabi Yau Algebras of dimension 3 are isomorphic to path algebras of quivers with relations derived from a superpotential. We show that for a given quiver $Q$ and a degree $d$, the set of good superpotentials of degree $d$, i.e. those that give rise to Calabi Yau algebras is either empty or almost everything (in the measure theoretic sense). We also give some constraints on the structure of quivers that allow good superpotentials, and for the simplest quivers we give a complete list of the degrees for which good superpotentials exist.

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