Extension of the main theorem to all symmetrizable Cartan matrices

Let $C$ be a symmetrizable generalized Cartan matrix, let $D$ be a symmetrizer of $C$, and let $H=H(C,D,\Omega)$, $\mathcal{M}=\mathcal{M}(H)$, and $\mathfrak{n}=\mathfrak{n}(C)$ be as in the paper. The main theorem for Dynkin type asserts that the primitive Lie algebra $\mathcal{P}(\mathcal{M})$ is isomorphic to $\mathfrak{n}$ and that

$$\eta_H\colon U(\mathfrak{n})\to\mathcal{M}$$

is an isomorphism of Hopf algebras. Extension of the main theorem. Theorem~ remains true for all symmetrizable generalized Cartan matrices $C$ and all symmetrizers $D$ of $C$. This is the same proposed extension of the Dynkin-type result to the general symmetrizable case; its resolution is not supplied here.