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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.
11
votes
Motivating the Casimir element
This is an old question, but I was reviewing this stuff and wanted to elaborate on Daniel Litt's answer to explain why we should expect the Casimir element to give a proof of Weyl's theorem.
General …