On Yang-Baxter equation and Calabi-Yau property of Koszul algebras

–A well-known result of Beidar, Fong, and Stolin yields a description of symmetric Frobenius algebras through solutions of the quantum Yang-Baxter equation. We will prove a graded version of this theorem and produce a new characterization of Koszul Calabi-Yau algebras. We give another proof of the Calabi-Yau property for three and four-dimensional Sklyanin algebras as an application.

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