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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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The orders of the exceptional Weyl groups
The orders of the Weyl groups of root systems of type $E_6$, $E_7$, $E_8$ seem to appear in a 1894 Comptes Rendus paper [1] of Cartan, pp. 641-642. The paper [2] has the details and the orders appear …