An Unexpected Cyclic Symmetry of $I{\mathfrak{u}}_n$

Abstract

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

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