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Extending the work of Braverman and Gaitsgory on the deformation of Koszul algebras and the Poincar{\\'e}-Birkhoff-Witt theorem we obtain a generalized Duflo isomorphism which is valid also over fields of finite characteristic: $H_{\\text{Lie}}^n(\\mathfrak g, S\\mathfrak g) \\cong H_{\\text{Hoch}}^n(U\\mathfrak g,U\\mathfrak g)$ for all $n < \\operatorname{char}\\mathbf k$. 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Extending the work of Braverman and Gaitsgory on the deformation of Koszul algebras and the Poincar{\\'e}-Birkhoff-Witt theorem we obtain a generalized Duflo isomorphism which is valid also over fields of finite characteristic: $H_{\\text{Lie}}^n(\\mathfrak g, S\\mathfrak g) \\cong H_{\\text{Hoch}}^n(U\\mathfrak g,U\\mathfrak g)$ for all $n < \\operatorname{char}\\mathbf k$. 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