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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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The action of $GL_{\infty}$ on the infinite wedge space
The normal action is defined for example in https://arxiv.org/pdf/alg-geom/9712009.pdf page 11. As well as Many other references including Kac papers.