Batalin–Vilkovisky algebras and the noncommutative Poincaré 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!A!. This confirms (a generalization of) a conjecture of R. Rouquier.