Monomial Gorenstein algebras and the stably Calabi–Yau property

A celebrated result by Keller–Reiten says that 2-Calabi–Yau tilted algebras are Gorenstein and stably 3-Calabi–Yau. This note shows that the converse holds in the monomial case: a 1-Gorenstein monomial algebra and stably 3-Calabi–Yau is 2-Calabi–Yau tilted, moreover is Jacobian. We study the case of other stably Calabi–Yau Gorenstein monomial algebras.