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- TL;DR Summary
- Is there a physical system which uses these groups?

I wonder whether there is a physical theory / model / example whatever, that uses one of the (Lie) groups ##\begin{bmatrix}1&a_2&\ldots&a_n\\0&1&\ldots&0\\ \vdots & \vdots &&\vdots \\0&0&\ldots&1 \end{bmatrix}## or the Lie algebra ##\begin{bmatrix}a_1&a_2&\ldots&a_n\\0&0&\ldots&0\\ \vdots & \vdots &&\vdots \\0&0&\ldots&0 \end{bmatrix}##?

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