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Results tagged with lie-algebras
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user 149493
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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Reference request: Serre relations for affine Lie algebras
Let $\hat{\mathfrak{g}} = L\mathfrak{g}\oplus \mathbb{C}K$ be the affine Lie algebra corresponding to a simple, finite-dimensional Lie algebra $\mathfrak{g}$. Many texts note that one can define the S …
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Reference request: Category of finite dimensional representations of loop algebra is not sem...
For $\mathfrak{g}$ a semisimple Lie algebra, we may define its (untwisted) loop algebra as $L(\mathfrak{g}) = \mathfrak{g} \otimes \mathbb{C}\lbrack t,t^{-1} \rbrack$. Let $\mathcal{F}$ be the categor …
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