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Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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Number of real forms of a (not semisimple, solvable) Lie algebra
Consider the Lie algebra $\mathfrak{r}_2=\mathfrak{aff}(\mathbb{C})$ of the group of affine maps of $\mathbb{C}$, and let $\mathfrak{g}=\mathfrak{r}_2 \oplus \mathfrak{r}_2$.
I am interested in knowin …