# 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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### The double cover in the classical limit of $U_q(\frak{sl}_2)$

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### Why does Kashiwara define $U_q(\mathfrak{g})$ over $\mathbb{Q}(q)$ rather than $\mathbb{C}(q)$?

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### Which representations of $\mathfrak{sl}(2)$ are tensor products of powers of irreducible representations?

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### Lie Groups and Lie algebras related to Jordan algebras

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### Classification of root lattice embeddings in $E_{10}$

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### Levi decomposition for associative algebras

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### What subspace of $\operatorname{SU}(4)$ group keeps an element of the $\mathfrak{su}(2)$ subalgebra within $\mathfrak{su}(2)$ upon adjoint action?

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### Primitive elements in Hopf algebras over the integers

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### The coherence property of center of universal enveloping algebra for reductive Lie algebra?

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### Spherical harmonics, $\frak{sl}_2$, and algebra gradings

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### Which infinite-dimensional Lie algebras have realizations as algebras of global sections of vector bundles with special structure?

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### Root system of fixed point Lie sub-algebra

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### Cohomology algebra of the maximal nilpotent subalgebra of a semisimple Lie algebra

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### The product of $Z(\mathfrak{g})$-finite functions is also $Z(\mathfrak{g})$-finite?

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### A specific coset decomposition of $\mathrm{GL}_n(\mathbb{C})$

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### What is the analogue of Leibniz's rule for universal enveloping algebra?

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### How can we prove a specific isomorphism between graded Lie algebra and graded universal enveloping algebra?

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### Explicit example of prime ideal not an intersection of maximal ideals, in universal enveloping algebra

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### Examples of indefinite Einstein non-Ricci-flat metric on solvmanifolds

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### What's the advantage of defining Lie algebra cohomology using derived functors?

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### Canonical parabolics vs Levi subgroups

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### Reference request for indecomposable representations of $\mathfrak{sl}(2)$ over an algebraically closed field of characteristic $p > 0$

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### Cartan subspace of graded Lie algebras

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### Singular del Pezzo surfaces and degeneration of root systems

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### Jordan decomposition for simple Lie algebra

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### Derivative of a representation

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### Alternate proof of easiest special case of PBW theorem

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### Are smooth Schubert varieties Kähler? [closed]

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### Commutators and brackets in nilpotent Lie algebras

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### Elements of the Hall basis described via permutations

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### Universal enveloping algebra of Malcev Lie algebra associated to nilpotent group

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### $G$-equivariant modules and Lie algebra cohomology

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### When is a nilpotent Lie algebra isomorphic to the associated graded of its lower central series?

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### Dimensions of $\frak{sl}_n$-representations

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### Derivation on $SO(3)$

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### Rigidity of Borel Lie algebras

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### Special orthonormal frame on $\mathbb{S}^3$

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### Equivalence classes of Hermitian elements in a central simple algebra with an involution of second kind

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### Find all finite dimensional simple quotients of a possibly infinite dimensional Lie algebra generated by three elements

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### Find all finite dimensional simple Lie algebras satisfying certain conditions

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### Showing the positivity of the determinant of $\mathfrak{sp}(n)$ without making use of diagonalization

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### Algebraic K-theory of enveloping algebras and PBW-algebras - a reference request

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### Non-cosemisimple duals of pointed Hopf algebras

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### The centralizer and normalizer of products of (SU(n) $\times$ SU(p) $\times$ …) in U(m)

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### Action of the Casimir on highest weight modules for Kac-Moody algebra

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### Isometry groups of symmetric spaces

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### Group-like elements of universal enveloping algebra

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### Schubert cells in G/P for reductive G

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### Why is this operator independent of the choice of basis

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