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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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Are maximal connected semisimple subgroups automatically closed?
If G is a simply connected Lie group and H a connected semisimple Lie subgroup then H is closed. Mostow Ann.Math. 1950, p. 615.