DERIVED INVARIANCE OF HIGHER STRUCTURES ON THE HOCHSCHILD COMPLEX

We show that derived equivalences preserve the homotopy type of the (cohomological) Hochschild complex as a B1-algebra. More generally, we prove that, as an object of the homotopy category of B1-algebras, the Hochschild complex is contravariant with respect to fully faithful derived tensor functors. We also show that the Hochschild complexes of a Koszul algebra and its dual are homotopy equivalent as B1-algebras. In particular, their Hochschild cohomologies are isomorphic as algebras, which is a recent result by R.-O. Buchweitz (4), and as Lie algebras. Our methods also yield a derived invariant definition of the Hochschild complex of an exact category.