The classification of 3-dimensional noetherian cubic Calabi-Yau algebras

2016/06/01 by Mori, Izuru, Ueyama, Kenta
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1606.00183

Abstract

It is known that every 3-dimensional noetherian Calabi-Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S. P. Smith and the first author classified all superpotentials whose Jacobian algebras are 3-dimensional noetherian quadratic Calabi-Yau algebras. The main result of this paper is to classify all superpotentials whose Jacobian algebras are 3-dimensional noetherian cubic Calabi-Yau algebras. As an application, we show that if S is a 3-dimensional noetherian cubic Calabi-Yau algebra and σ is a graded algebra automorphism of S, then the homological determinant of σ can be calculated by the formula hdet σ=(det σ)² with one exception.

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