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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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Is it possible to compute the Iwahori Decomposition using the Chavalley Commutator Formulas?
Ideally, I would like a constructive, algorithmic proof of this fact. I have convinced myself that it is true, but my "proof" is not pretty. I would like to know if a more attractive or intuitive proo …