  We find and discuss an unexpected (to us) order $n$ cyclic group of
automorphisms of the Lie algebra $I\mathfrak{u}_n :=
\mathfrak{u}_n\ltimes\mathfrak{u}_n^\ast$, where $\mathfrak{u}_n$ is the Lie
algebra of upper triangular $n\times n$ matrices. Our results also extend to
$gl_{n+}^\epsilon$, a ``solvable approximation'' of $gl_n$, as defined within.
