We find and discuss an unexpected (to us) order n cyclic group of automorphisms of the Lie algebra \(I{\mathfrak u}_n{:}{=}{\mathfrak u}_n < imes {\mathfrak u}_n^*\), where \({\mathfrak u}_n\) is the Lie algebra of upper triangular \(n\times n\) matrices. Our results also extend to \(\mathfrak {gl}_{n+}^\epsilon \), a “solvable approximation” of \(\mathfrak {gl}_n\), as defined within.

中文翻译：

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$$I{\mathfrak u}_n$$ 的意外循环对称

我们发现并讨论了李代数\(I{\mathfrak u}_n{:}{=}{\mathfrak u}_n < imes {\mathfrak u}_n^ *\)，其中\({\mathfrak u}_n\)是上三角\(n\times n\)矩阵的李代数。我们的结果还扩展到\(\mathfrak {gl}_{n+}^\epsilon \) ，这是\(\mathfrak {gl}_n\)的“可求解近似值” ，定义如下。