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15
61
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Why does the definition of cocyle in a central extension of a Lie algebra work?

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#lie-algebras #homology-cohomology #semisimple-lie-algebras #central-extensions
118
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The Lie algebra of zariski closure of an algebraic group.

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#group-theory #algebraic-geometry #lie-groups #lie-algebras #zariski-topology
127
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If $\alpha, \beta, \alpha + \beta \in \Phi$ then $[L_{\alpha} , L_{\beta}] = L_{\alpha + \beta}.$

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#lie-algebras #root-systems #semisimple-lie-algebras
95
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Sublattice of the weight lattice

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#lie-algebras #root-systems #semisimple-lie-algebras
46
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How to find the isomorphism between Lie algebra $L_{0}$ and $L_{1}$?

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#manifolds #lie-groups #lie-algebras #vector-fields #vector-space-isomorphism
94
Views

curvature tensor of symmetric spaces

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#riemannian-geometry #lie-groups #lie-algebras #semisimple-lie-algebras #symmetric-spaces
48
Views

Proof of the fact that $\mathfrak{g}\otimes C^{\infty}(S^1) \cong C^{\infty}(S^1;\mathfrak{g})$

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#manifolds #lie-algebras #tensor-products #complex-manifolds
131
Views

How to exponentiate the vector field $v$?

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#differential-geometry #lie-groups #lie-algebras #exponentiation #vector-fields
91
Views

Is there a canonical coordinate representation for Lie algebras?

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#differential-geometry #lie-algebras #vector-fields
82
Views

Elements of the coset $G/H$, where $G=\text{GL}^+(2)$ and $H=\text{SO}(2)$

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#group-theory #lie-groups #lie-algebras
130
Views

Given the Coxeter-Dynkin Diagram of a Lie-Algebra, how do we build the Satake-Tits diagrams of the group's real forms?

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#lie-groups #lie-algebras #coxeter-groups #dynkin-diagrams
65
Views

Problem in understanding a fact about Lie algebra.

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#lie-algebras #direct-sum #root-systems #semisimple-lie-algebras
110
Views

Simple roots of E6 root system

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#lie-algebras #root-systems
350
Views

Computing the Right Jacobian on Lie Group

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#multivariable-calculus #lie-groups #lie-algebras #rotations #jacobian
38
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why is a Lie algebra not nilpotent even if an ideal is nilpotent and algebra quotient by ideal is nilpotent

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#lie-algebras #ideals #quotient-spaces #nilpotence

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