Question

Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

score 2.3k · Answer 1 · 2026-03-25 22:06:14

2.3k

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Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

Published on 25 Mar 2026 - 22:06

score 125 · Answer 2 · 2014-12-29 16:22:12

125

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Inductively prove that $L_{\mathbb{X}}i_\mathbb{Y}=i_{[\mathbb{X},\mathbb{Y}]}+i_\mathbb{Y}L_{\mathbb{X}} $

Published on 29 Dec 2014 - 16:22

score 1.3k · Answer 3 · 2026-03-25 09:26:59

1.3k

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Weyl groups: correspondence of reflections and roots?

Published on 25 Mar 2026 - 9:26

score 274 · Answer 4 · 2026-04-03 22:15:17

274

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Does the adjoint action induce a trivial action on Lie algebra cohomology?

Published on 03 Apr 2026 - 22:15

score 94 · Answer 5 · 2026-03-25 17:21:29

94

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Lie algebra of a semi-direct product of Lie groups

Published on 25 Mar 2026 - 17:21

score 39 · Answer 6 · 2026-03-26 12:47:00

39

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What controls the central extensions of Lie algebras when the Lie Group is not compact?

Published on 26 Mar 2026 - 12:47

score 2.7k · Answer 7 · 2026-03-25 17:20:02

2.7k

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Describing the Lie algebra structure of a semi-direct product of Lie groups

Published on 25 Mar 2026 - 17:20

score 52 · Answer 8 · 2026-03-30 14:41:14

52

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Homotopy of right action on left-invariant differential forms

Published on 30 Mar 2026 - 14:41

score 351 · Answer 9 · 2026-04-03 04:39:07

351

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Relation between $SO\left(1,3\right)$ and $SU\left(2\right)$

Published on 03 Apr 2026 - 4:39

score 372 · Answer 10 · 2026-04-03 06:06:09

372

Views

On equation $exp [X,Y]=[exp X,exp Y]$ on a Lie group and its Lie algebra

Published on 03 Apr 2026 - 6:06

score 225 · Answer 11 · 2026-04-03 06:03:58

225

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Non-surjectivity of exponential map: how to understand?

Published on 03 Apr 2026 - 6:03

score 70 · Answer 12 · 2026-04-03 06:10:57

70

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Several questions about Lie groups and algebras

Published on 03 Apr 2026 - 6:10

score 606 · Answer 13 · 2019-10-07 18:28:30

606

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Tensor product of two irreducible $\mathfrak sl_2$ modules

Published on 07 Oct 2019 - 18:28

score 105 · Answer 14 · 2026-03-30 03:38:30

105

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Second cohomology group $H^2(\mathfrak{g},\mathbb{R})$ of a semisimple Lie algebra

Published on 30 Mar 2026 - 3:38

score 808 · Answer 15 · 2019-10-08 12:35:39

808

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Associative Lie algebra

Published on 08 Oct 2019 - 12:35

List Question

Why are root spaces of root decomposition of semisimple Lie algebra 1 dimensional?

Inductively prove that $L_{\mathbb{X}}i_\mathbb{Y}=i_{[\mathbb{X},\mathbb{Y}]}+i_\mathbb{Y}L_{\mathbb{X}} $

Weyl groups: correspondence of reflections and roots?

Does the adjoint action induce a trivial action on Lie algebra cohomology?

Lie algebra of a semi-direct product of Lie groups

What controls the central extensions of Lie algebras when the Lie Group is not compact?

Describing the Lie algebra structure of a semi-direct product of Lie groups

Homotopy of right action on left-invariant differential forms

Relation between $SO\left(1,3\right)$ and $SU\left(2\right)$

On equation $exp [X,Y]=[exp X,exp Y]$ on a Lie group and its Lie algebra

Non-surjectivity of exponential map: how to understand?

Several questions about Lie groups and algebras

Tensor product of two irreducible $\mathfrak sl_2$ modules

Second cohomology group $H^2(\mathfrak{g},\mathbb{R})$ of a semisimple Lie algebra

Associative Lie algebra

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