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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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Twisted affine Lie algebras
In the Chapter 8 of Kac's book about Kac-Moody algebras there is a theorem which guarantee that we can work only with diagram automorphisms to construct twisted affine algebras.
Specifically, he prove …