Question

For $\mathfrak{g}$ semisimple, is $[\mathfrak{g}, \mathfrak{g}] = \mathfrak{g}$.

score 271 · Answer 1 · 2026-03-27 15:17:58

271

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For $\mathfrak{g}$ semisimple, is $[\mathfrak{g}, \mathfrak{g}] = \mathfrak{g}$.

Published on 27 Mar 2026 - 15:17

score 759 · Answer 2 · 2026-03-25 10:58:57

759

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What is the relationship between the radical of the Killing form and the radical of a Lie algebra?

Published on 25 Mar 2026 - 10:58

score 117 · Answer 3 · 2026-03-27 16:55:20

117

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If $\mathfrak{g} / I$ is semisimple, then is $\mathrm{rad}(\mathfrak{g}) \subset I$?

Published on 27 Mar 2026 - 16:55

score 132 · Answer 4 · 2019-05-28 12:13:02

132

Views

Is the image of an ideal under a surjective Lie algebra homomorphism an ideal?

Published on 28 May 2019 - 12:13

score 84 · Answer 5 · 2026-03-29 10:08:47

Concrete example of Lie algebra $\mathfrak{g}$ with $x$ s.t. $x$ is in the radical of $\mathfrak{g}$ but not the radical of the Killing form?

score 728 · Answer 6 · 2026-03-25 12:28:07

728

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Why is the Killing form of $\mathfrak{g}$ restricted to a subalgebra $\mathfrak{a} \subset \mathfrak{g}$ not the Killing form of $\mathfrak{a}$?

Published on 25 Mar 2026 - 12:28

score 124 · Answer 7 · 2026-03-26 07:42:28

124

Views

Simple Lie Algebra + $Z(G) = \{1\}$ $\Rightarrow$ Simple Lie Group.

Published on 26 Mar 2026 - 7:42

score 284 · Answer 8 · 2019-05-28 21:14:01

284

Views

Nilpotent Lie Algebras: Irreducible Representations

Published on 28 May 2019 - 21:14

score 94 · Answer 9 · 2026-03-25 17:23:39

94

Views

Universal enveloping algebra and the Rees ring

Published on 25 Mar 2026 - 17:23

score 234 · Answer 10 · 2026-03-27 16:46:28

234

Views

Comparison of Casimir elements

Published on 27 Mar 2026 - 16:46

score 252 · Answer 11 · 2026-03-25 01:15:21

252

Views

Reduced Expression for Reflection in Weyl Group

Published on 25 Mar 2026 - 1:15

score 238 · Answer 12 · 2026-03-27 13:45:41

238

Views

$\mathfrak{sl}_4(\mathbb{C})$ is semisimple

Published on 27 Mar 2026 - 13:45

score 47 · Answer 13 · 2019-06-05 08:27:50

47

Views

Commutativity and direct sum decomposition of Lie Algebras

Published on 05 Jun 2019 - 8:27

score 219 · Answer 14 · 2026-03-25 23:36:41

219

Views

Which vectors are weight vectors for some Cartan subalgebra?

Published on 25 Mar 2026 - 23:36

score 56 · Answer 15 · 2026-03-30 03:55:42

56

Views

Induced Lie structure on the tanget space of a Lie group at the identity element.

Published on 30 Mar 2026 - 3:55

List Question

For $\mathfrak{g}$ semisimple, is $[\mathfrak{g}, \mathfrak{g}] = \mathfrak{g}$.

What is the relationship between the radical of the Killing form and the radical of a Lie algebra?

If $\mathfrak{g} / I$ is semisimple, then is $\mathrm{rad}(\mathfrak{g}) \subset I$?

Is the image of an ideal under a surjective Lie algebra homomorphism an ideal?

Concrete example of Lie algebra $\mathfrak{g}$ with $x$ s.t. $x$ is in the radical of $\mathfrak{g}$ but not the radical of the Killing form?

Why is the Killing form of $\mathfrak{g}$ restricted to a subalgebra $\mathfrak{a} \subset \mathfrak{g}$ not the Killing form of $\mathfrak{a}$?

Simple Lie Algebra + $Z(G) = \{1\}$ $\Rightarrow$ Simple Lie Group.

Nilpotent Lie Algebras: Irreducible Representations

Universal enveloping algebra and the Rees ring

Comparison of Casimir elements

Reduced Expression for Reflection in Weyl Group

$\mathfrak{sl}_4(\mathbb{C})$ is semisimple

Commutativity and direct sum decomposition of Lie Algebras

Which vectors are weight vectors for some Cartan subalgebra?

Induced Lie structure on the tanget space of a Lie group at the identity element.

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