Abstract

To a g-manifold, a smooth manifold with a Lie algebra action, one can associate two dglas which play roles similar to the spaces of polyvector fields and polydifferential operators. We establish the formality theorem for g-manifolds, i.e., an L∞ quasi-isomorphism from the dgla analogous to polyvector fields to the dgla analogous to polydifferential operators. As an application, we obtain a Kontsevich–Duflo type theorem for g-manifolds. The parallel theorems for other cases will also be mentioned briefly.