Question

How to show this $L$-module is simple? (related to the root space decomposition of semisimle Lie algebras)

score 272 · Answer 1 · 2026-03-27 12:03:15

272

Views

How to show this $L$-module is simple? (related to the root space decomposition of semisimle Lie algebras)

Published on 27 Mar 2026 - 12:03

score 212 · Answer 2 · 2026-03-25 09:36:34

212

Views

KIlling vectors from isometries and orbit spaces

Published on 25 Mar 2026 - 9:36

score 159 · Answer 3 · 2019-03-06 05:47:13

159

Views

How to show a vector space is a real form of another?

Published on 06 Mar 2019 - 5:47

score 27 · Answer 4 · 2026-03-27 12:07:10

27

Views

Question about definition related to root system of semisimple Lie algebras

Published on 27 Mar 2026 - 12:07

score 58 · Answer 5 · 2019-03-08 23:07:32

58

Views

Show $\left<h\right>_{\mathbb{C}}$ is a Cartan subalgebra of $\mathfrak{sl}\left( 2,\mathbb{C}\right)$.

Published on 08 Mar 2019 - 23:07

score 216 · Answer 6 · 2026-03-25 13:57:07

216

Views

Riemannian metric and Laplacian coming from an invariant form on the lie algebra

Published on 25 Mar 2026 - 13:57

score 28 · Answer 7 · 2019-03-09 16:34:02

28

Views

Question regarding the definition of the action of $sl_2$ on a vector space

Published on 09 Mar 2019 - 16:34

score 99 · Answer 8 · 2019-03-09 21:58:33

99

Views

Representation of Lie algebra of germs of smooth/holomorphic functions

Published on 09 Mar 2019 - 21:58

score 122 · Answer 9 · 2019-03-10 03:59:59

122

Views

Conjugacy of Borel Subalgebras: Proof in Humphreys' Introduction to Lie Algebras and Representation Theory

Published on 10 Mar 2019 - 3:59

score 91 · Answer 10 · 2019-03-10 07:27:43

91

Views

name of Lie group $\text{SU}(2) \times \text{SU}(2) \times \text{SU}(2)/\mathbb{Z}_2$

Published on 10 Mar 2019 - 7:27

score 49 · Answer 11 · 2019-03-10 18:10:13

49

Views

Show $H \cap L_i$ is a Cartan subalgebra of $L_i$

Published on 10 Mar 2019 - 18:10

score 67 · Answer 12 · 2026-03-27 12:03:14

67

Views

"If $g$ is semisimple, It is not too hard to see that $H^2(g,a)=0$. With a little supplementary argument..."

Published on 27 Mar 2026 - 12:03

score 55 · Answer 13 · 2019-03-11 12:42:37

55

Views

Proof of Weyl Character formula for $sl_n\mathbb{C}$

Published on 11 Mar 2019 - 12:42

score 66 · Answer 14 · 2019-03-13 13:31:44

66

Views

Intuition behind adjoint map

Published on 13 Mar 2019 - 13:31

score 594 · Answer 15 · 2026-03-25 09:39:57

594

Views

Lie bracket of canonical vectors on tangent space to a point on a manifold is zero.

Published on 25 Mar 2026 - 9:39

List Question

How to show this $L$-module is simple? (related to the root space decomposition of semisimle Lie algebras)

KIlling vectors from isometries and orbit spaces

How to show a vector space is a real form of another?

Question about definition related to root system of semisimple Lie algebras

Show $\left<h\right>_{\mathbb{C}}$ is a Cartan subalgebra of $\mathfrak{sl}\left( 2,\mathbb{C}\right)$.

Riemannian metric and Laplacian coming from an invariant form on the lie algebra

Question regarding the definition of the action of $sl_2$ on a vector space

Representation of Lie algebra of germs of smooth/holomorphic functions

Conjugacy of Borel Subalgebras: Proof in Humphreys' Introduction to Lie Algebras and Representation Theory

name of Lie group $\text{SU}(2) \times \text{SU}(2) \times \text{SU}(2)/\mathbb{Z}_2$

Show $H \cap L_i$ is a Cartan subalgebra of $L_i$

"If $g$ is semisimple, It is not too hard to see that $H^2(g,a)=0$. With a little supplementary argument..."

Proof of Weyl Character formula for $sl_n\mathbb{C}$

Intuition behind adjoint map

Lie bracket of canonical vectors on tangent space to a point on a manifold is zero.

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