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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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What is the (Koszul? derived?) interpretation of a pair of Lie algebras with the same cohomo...
You (and "everyone") may already know this, but there is a really simple answer to a variant of your question, that is when instead of starting with a Lie algebra you start with a connected differenti …