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Basis of Clifford algebra

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#riemannian-geometry #lie-algebras #clifford-algebras
327
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Is the theorem of complete reducibility or the abstract Jordan decomposition needed for structure theory of semisimple Lie algebras?

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#lie-algebras
134
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Real representations of Lie groups

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#reference-request #representation-theory #lie-groups #lie-algebras
753
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Spin(4,1) = Sp(1,1) isomorphism

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#lie-groups #lie-algebras #quaternions #exceptional-isomorphisms #classical-groups
2.2k
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Lie algebra of the two dimensional torus

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#differential-geometry #manifolds #lie-algebras
178
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Lie group representation $\rho$ completely reducible iff $d\rho$ is completely reducible

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#representation-theory #lie-groups #lie-algebras
64
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Space of derivations that give a Lie algebra

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#abstract-algebra #lie-algebras #jacobian
163
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Some details in proof of SO(n) is product of reflection

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#matrices #lie-groups #riemannian-geometry #lie-algebras
867
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Is there a classification of non-compact Lie Groups? I am interested specifically in subgroups of GL(n,R).

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#group-theory #lie-groups #lie-algebras
106
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Let $G$ be Lie group. Show that $\left.d\left(L_{exp(X)^{-1}}\circ \exp\right)\right|_{X}Y= \frac{1+\exp(\mbox{ad}(X))}{\mbox{ad}(X)}(Y)$

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#differential-geometry #lie-groups #lie-algebras
1.2k
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Show that the Lie algebra generated by x, y with relations $ad(x)^2(y) = ad(y)^5(x) = 0$ is infinite dimensional and construct a basis

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#representation-theory #lie-algebras
136
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Regarding lower central series of a Lie algebra L

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#lie-algebras
106
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The definition of the Killing form

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#lie-algebras
36
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Why is the following derivation on differential map between 2 Riemannian manifold valid?

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#lie-groups #riemannian-geometry #lie-algebras #fiber-bundles
558
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Please suggest YouTube lecture on Lie algebra

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#soft-question #lie-groups #lie-algebras

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