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Ideals of semisimple Lie algebras

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#lie-algebras #semisimple-lie-algebras
3.8k
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Why do $SU(2)$ and $SL(2,\mathbb{C})$ have the same Lie algebra?

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#group-theory #lie-groups #lie-algebras #dynkin-diagrams
79
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Show that given an irreducible module of heighest weight $0$ over a lie algebra has dimension $1$

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#linear-algebra #abstract-algebra #lie-algebras
614
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Lie algebra normalizer centralizer

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#lie-algebras
78
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Which groups $H$ act transitively on a noncompact symmetric space $G/K$?

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#lie-groups #lie-algebras #homogeneous-spaces #symmetric-spaces
55
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A particular connection on the group

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#lie-groups #riemannian-geometry #lie-algebras #connections
116
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$AB - BA = \lambda B$ has a nontrivial solution, iff $\lambda = \lambda_i - \lambda_j$?

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#linear-algebra #lie-algebras
59
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If $H$ acts transitively on $G/K$, does it contain a copy of $AN$?

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#lie-groups #lie-algebras #homogeneous-spaces #symmetric-spaces
47
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A question about the existence of Lie vector field

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#differential-geometry #lie-groups #riemannian-geometry #lie-algebras #lie-derivative
27
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Submodule of a space of 2-vector fields

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#differential-geometry #modules #lie-algebras
416
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Computing Casimir basis functions for Lie algebra $so(4)$ (via Killing form)

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#representation-theory #lie-groups #lie-algebras
505
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The unit group of a finite dimensional associative algebra is a Lie group?

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#abstract-algebra #lie-groups #lie-algebras
75
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Explicit construction of $SO(3)$ elements from $SU(2)$ and $\mathfrak{su}(2)$

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#group-theory #lie-groups #lie-algebras
369
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Infinite-dimensional representation theory

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#representation-theory #lie-groups #lie-algebras
53
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Question in Section F.2 of Fulton & Harris

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#lie-groups #lie-algebras #matrix-calculus

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