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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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Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials?
Non-negativity is important in the proof of Lusztig's 15 conjectures (in fact, it is easy to be proved with the non-negativity property, like in the "split case" and "quasi-split case"). Although even …