# 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.

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### Checking axiom of Category $\mathcal{O}$

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### Regarding $F_4$ and $G_2$ Lie algebras, do there exist $F_n$ or $G_n$ families of Lie algebras?

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### BGG Category $\mathcal{O}$ is not closed under extension

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### Obstruction to the existence of an invariant symplectic connection

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### An extension of symplectomorphism group

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### Proof of parametrisation of $\hat{\mathfrak{g}}$-intertwiners of induced modules of affine Lie algebras

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### Confusion over spin representation and coordinate ring of orthogonal Grassmannian

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### Cohomology and higher structures

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### A transversal for the $\operatorname{Ad}(K)$ action on a sphere in $\mathfrak{p}$

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### Continuity/Lipschitz regularity of exponential map from $C_c$ to $\operatorname{Diff}_c$?

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### Hopf algebras structure and quantum affine algebras

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### Is a 8-dimensional quadratic form recognized by its Lie algebra, modulo equivalence and scalar multiplication?

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### Composition of operators in $w_{1+\infty}$ and $W_{1+\infty}$

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### Existence of a maximal rank CR Lie subalgebra

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### Complete reducibility of integrable modules over symmetrizable Kac-Moody Lie algebras

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### Classification of symplectic resolutions

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### Lifting one parameter subgroup $e^{t K}$ to the universal cover of $\mathrm{Sp}(2N,\mathbb{R})$

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### Reference request: Category of finite dimensional representations of loop algebra is not semisimple

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### Maximal quotients of the enveloping algebra of a simple Lie algebra

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### Is there a functorial relation of center of universal enveloping algebra?

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### Lie algebra cohomology: $H^i(R,V)=H^i(R,V^R)$ with $R$ reductive and $V$ an $R$-module

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### Relation between topological and differentiable Lie group cohomology for unitary modules

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### Choosing a complementary Lie subalgebra well

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### Algebra of regular functions on the quadratic cone and SU(2) representations

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### Closed subgroup (Cartan) theorem without transversality nor Lipschitz condition within Banach algebras

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### Question on the center of universal enveloping algebra

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### Classification of involutions on $G_{2}$-homogeneous spaces

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### Connectedness of the stabilizer in a semisimple group of a semisimple element in the Lie algebra: a reference request

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### The Lie algebra of the subgroup of $GL(n)$ preserving a given variety

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### When a finite codimensional subalgebra contains a finite codimension ideal?

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### Did anybody come across this Lie algebra representation?

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### Do rational points in a split reductive group act transitively on the orbits of the Cartan subalgebra (w.r.t. automorphism group of Lie algebra)?

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### Explicit branching rules from $G(n+m)$ to $G(n) \times G(m)$ (where $G = \operatorname{SL}$, $\operatorname{SO}$ or $\operatorname{Sp}$)

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### Matrix Lie algebra: Semisimple element = semisimple matrix?

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### Nontrivial Poisson relations for affine Poisson algebras

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### Ideal of the free Lie algebra L(x,y) generated by x

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### Weight space dimension of the fundamental representation $\pi_n$ for type $C_n$

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### Invariant complex structures for simple Lie groups

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### Property of a semisimple Lie algebra over complex number field

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### Examples of simple vertex operator algebras (VOAs)

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### A conjecture about the barycenter of a polytope

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### Maximal dimension of abelian subalgebra of exceptional simple Lie algebra in positive characteristic

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### Homotopy Gerstenhaber algebras: description via operads vs derivations

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### Understanding the geometric fibre twisted differential operators

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### Embedding of Verma modules in Kac-Moody Lie algebras

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### What are Harish-Chandra bimodules used for?

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### Algorithm to construct basis for Kac-Moody algebra

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### Baker–Campbell–Hausdorff formula for exponential of general Hermitian operators

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### Quantum Hamiltonian reduction and tensor products

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