Most of the introductions into Lie algebras start with the notion of a two-dimensional non-abelian Lie algebra $\mathfrak{g} = \langle x,y\rangle$ such that $[x,y]=x$. Is there a common notation for this one?
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It is the Lie algebra of the affine group in 1-dimension. I've seen it written as $\mathfrak{aff}(1)$. See here for example – Callum Nov 10 '23 at 11:37
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In the French literature (and also in others) it is $\mathfrak{r}_2(K)$, where the "r" stands for "resoluble", which means solvable. And $K$ is an arbitrary field. See for example here. – Dietrich Burde Nov 11 '23 at 11:28
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@Callum Thanks! – Matthew Willow Nov 15 '23 at 22:21
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@DietrichBurde Thank you! – Matthew Willow Nov 15 '23 at 22:22