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This note extends the Steinberg Tensor product theorem from the Frobeniuskernel $G_{(r)}$ to the deformation $\mathcal{U}^{[r]}(\mathfrak{g})$ of itsdistribution algebra. As a Corollary we proof some conjectures from \cite{Wes}.Further it describes the graded representation theory of$\mathcal{U}^{[r]}(\mathfrak{g})$ at a generic semisimple p-central characteras a twist of the category of graded $G_{(r-1)}$-modules. We conclude byexplaining this relation for $SL_2$ explicitely as well as computing the centerin this case.

Toward partial Verma functors of $\mathcal{U}^{[r]}(\mathfrak{g})$ and related results