Batalin-Vilkovisky algebras and the noncommutative Poincare duality of Koszul Calabi-Yau algebras

Let $A$ be a Koszul Calabi-Yau algebra. We show that there exists an isomorphism of Batalin-Vilkovisky algebras between the Hochschild cohomology ring of $A$ and that of its Koszul dual algebra $A^{!}$. This confirms (a generalization of) a conjecture of R.~Rouquier.