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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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On q-Demazure operators
Dear Chuck Hague,
It may not answer your question. But let me suggest you to take a look at sections 4.5, 5.3 and 5.4 of:
A. Joseph, Modules with a Demazure flag. Studies in Lie theory, 131–169, Pro …