A criterion for homogeneous potentials to be 3-Calabi-Yau

Abstract

We give a necessary and sufficient condition for an N-Koszul algebra defined by a homogeneous potential, to be 3-Calabi-Yau. As an application, we recover two families of 3-Calabi-Yau algebras recently appeared in the literature, by studying skew polynomial algebras over non-commutative quadrics.

Theorem 1.1 and its proof are revised. Minor corrections in the rest of the text

References in corpus (2)

• Calabi-Yau algebras
• A 3-Calabi-Yau algebra with G_2 symmetry constructed from the octonions