Kontsevich--Duflo theorem for Lie pairs

摘要: The Kontsevich--Duflo theorem states that, for any complex manifold $X$, the Hochschild--Kostant--Rosenberg map twisted by square root of Todd class tangent bundle $X$ is an isomorphism associative algebras from sheaf cohomology $H^{\bullet}(X,\Lambda T_X)$ to Hochschild $HH^{\bullet}(X)$. In this paper, we prove beyond sole manifolds, holds in a very wide range geometric contexts admitting description terms Lie algebroids, which include foliations and manifolds endowed with group action. More precisely, pairs. Every pair $(L,A)$, i.e. data subalgebroid $A$ algebroid $L$, gives rise two Gerstenhaber $H^{\bullet}_{\operatorname{CE}}(A,\mathcal{X}_{\operatorname{poly}}^{\bullet})$ $H^{\bullet}_{\operatorname{CE}}(A,\mathcal{D}_{\operatorname{poly}}^{\bullet})$ playing role similar spaces polyvector fields polydifferential operators. We that between these algebras.