  Let ${\mathcal B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of
diagonal type with braiding matrix $\mathfrak{q}$, let
$\mathcal{L}_{\mathfrak{q}}$ be the corresponding Lusztig algebra as in
arXiv:1501.04518 and let $\operatorname{Fr}_{\mathfrak{q}}:
\mathcal{L}_{\mathfrak{q}} \to U(\mathfrak{n}^{\mathfrak{q}})$ be the
corresponding quantum Frobenius map as in arXiv:1603.09387. We prove that the
finite-dimensional Lie algebra $\mathfrak{n}^{\mathfrak{q}}$ is either 0 or
else the positive part of a semisimple Lie algebra
$\mathfrak{g}^{\mathfrak{q}}$ which is determined for each $\mathfrak{q}$ in
the list of arXiv:math/0605795.
