  Using new configuration spaces, we give an explicit construction that extends
Kontsevich's Lie-infinity quasi-isomorphism from polyvector fields to
Hochschild cochains to a quasi-isomorphism of A-infinity algebras equipped with
actions by homotopy derivations of the Lie algebra of polyvector fields. One
may term this formality a formality of two-colored noncommutative Gerstenhaber
homotopy algebras. In our result the action of polyvector fields by homotopy
derivations of the wedge product on polyvector fields is not the adjoint action
by the Schouten bracket, but a homotopy nontrivial and, in a sense, unique
deformation of that action. As an application we give an explicit Duflo-type
construction for Lie-infinity algebras that generalizes the Duflo-Kontsevich
isomorphism between the Chevalley-Eilenberg cohomology of the symmetric algebra
on a Lie algebra and the Chevalley-Eilenberg cohomology of the universal
enveloping algebra of the Lie algebra.

Quantum Algebra