# Questions tagged [lie-algebras]

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. See also the [Wiki page](http://en.wikipedia.org/wiki/Lie_algebra).

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### Finding function $g$ related to given harmonic $ f$ in a certain way

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### Reference Request: Carnot Group Not Containing Group of Isometries

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### Lie Algebra of Automorphism Group of $\mathbb{P}_k^1$

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### First adjoint cohomology space of simple Lie algebras

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### Distance between Verma modules in certain “strongly” standard filtrations

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### Symmetry of Casimirs of Lie algebras

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### Panyushev's conjectured duality for root poset antichains

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### Central extensions, contractions and deformations

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### For a fixed dominant weight $\lambda$, are almost all dominant weights in the same coset above it?

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### About reductive Levi subalgebra of a parabolic subalgebra

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### About the setting of the book “Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$”

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### Weyl Group Element $w$ fixing a root, and its presentation as product of simple reflections $w=s_1\dots s_n$

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### Existence of a weight of a representation in the fundamental Weyl chamber

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### Homology of solvable (nilpotent) Lie algebras

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