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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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Non-semisimple Lie groups and Higgs bundles
There is a (related but not quite the same) construction which is valid for any Lie group $G$ and any closed (hence Lie) subgroup $H\subset G$ over any smooth base manifold $X$ which may be helpful.
O …