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.

中文翻译：

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Monomial Gorenstein代数和稳定的Calabi–Yau性质

凯勒-赖滕（Keller-Reiten）的一个著名结果表明，2-Calabi-Yau倾斜的代数是Gorenstein且稳定地是3-Calabi-Yau。该注释说明在单项式情况下反之成立：1-Gorenstein单项代数和稳定的3-Calabi–Yau是2-Calabi–Yau的倾斜，此外是Jacobian。我们研究了其他稳定的Calabi–Yau Gorenstein单项代数的情况。