At the suggestion of Joseph Bernstein, Braverman and Gaitsgory proved certain fundamental theorems on the deformation of Koszul algebras from which they showed that the the universal enveloping algebra, $U g$ of a finite dimensional Lie algebra $g$over an arbitrary field $k$ is a deformation of the symmetric algebra $S g$ on $g$; the Poincar{e´-Birkhoff-Witt theorem, is an immediate corollary. By extending the work of Braverman and Gaitsgory, we obtain a generalized Duflo isomorphism which is valid also over fields of finite characteristic: The cohomology $H_[{Lie}}^n( g, g)$ is isomorphic to $H_{{Hoch}}^n(U g,U g)$ for all n < the characteristic of $k$. This implies, in particular, that Duflo´s classic theorem, which is the special case in characteristic zero of dimension zero, in fact holds in all characteristics.