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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.

Dualit\'e de Van den Bergh et Structure de Batalin-Vilkovisky sur les alg\`ebres de Calabi-Yau