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The abstract notion of Tamarkin-Tsygan calculus with duality gives Batalin-Vilkovisky structures in a general setting. We apply this technique to the caseof Van den Bergh duality for algebras to prove that Calabi-Yau algebras areBV-algebras.

Dualité de Van den Bergh et structure de Batalin–Vilkoviskiĭ sur les algèbres de Calabi–Yau