Question

Why is there a factor of $2$ in the isomorphism $\operatorname{Lie}(S^3)\cong\mathbb{R}^3$?

score 82 · Answer 1 · 2026-03-28 05:23:25

82

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Why is there a factor of $2$ in the isomorphism $\operatorname{Lie}(S^3)\cong\mathbb{R}^3$?

Published on 28 Mar 2026 - 5:23

score 129 · Answer 2 · 2020-07-10 04:46:26

129

Views

Prove that $[X, Y] = \frac{\partial^2}{\partial s \partial t} \bigg|_{0} \left[\text{exp}(sX), \text{exp}(tY)\right]$ in a Lie group

Published on 10 Jul 2020 - 4:46

score 168 · Answer 3 · 2026-03-27 21:18:05

168

Views

Fundamental groups of coset spaces

Published on 27 Mar 2026 - 21:18

score 220 · Answer 4 · 2026-03-25 08:06:57

220

Views

$PSl_n(\mathbb{C})\cong PGl_n(\mathbb{C})$?

Published on 25 Mar 2026 - 8:06

score 126 · Answer 5 · 2026-02-23 17:26:12

126

Views

Heisenberg Lie group, image of specific element by any representation is nilpotent

Published on 23 Feb 2026 - 17:26

score 208 · Answer 6 · 2020-07-11 15:29:06

208

Views

Why is the image of a faithful representation of a Lie group a Lie subgroup?

Published on 11 Jul 2020 - 15:29

score 195 · Answer 7 · 2020-07-12 11:50:22

195

Views

Cardinalities of set of equivalence classes of Lie groups' and algebras' representations.

Published on 12 Jul 2020 - 11:50

score 308 · Answer 8 · 2020-07-12 12:01:35

308

Views

First prolongation formula

Published on 12 Jul 2020 - 12:01

score 220 · Answer 9 · 2026-03-27 00:05:10

220

Views

The projection $G\rightarrow G/H$ is a fibre bundle with structure group $N(H)/H$?

Published on 27 Mar 2026 - 0:05

score 161 · Answer 10 · 2020-07-12 16:25:39

161

Views

Dimension of SO(5)

Published on 12 Jul 2020 - 16:25

score 139 · Answer 11 · 2026-04-05 09:00:11

139

Views

Cotangent bundle of $SO(3)$

Published on 05 Apr 2026 - 9:00

score 25 · Answer 12 · 2020-07-12 20:39:12

25

Views

Jordan decomposition and vector fields

Published on 12 Jul 2020 - 20:39

score 83 · Answer 13 · 2020-07-12 21:04:37

83

Views

The exponential map is neither injective nor surjective when $n\ge 2$?

Published on 12 Jul 2020 - 21:04

score 141 · Answer 14 · 2026-03-27 21:19:25

141

Views

The neighborhood $U$ of the identity generates a connected Lie group $G$. Proof check.

Published on 27 Mar 2026 - 21:19

score 153 · Answer 15 · 2026-03-27 21:20:30

153

Views

$\operatorname{U}(2n) \supset \frac{\operatorname{Sp}(n) \times \operatorname{Sp}(m)}{\mathbb{Z}_2}$ for what maximum of $m$?

Published on 27 Mar 2026 - 21:20

List Question

Why is there a factor of $2$ in the isomorphism $\operatorname{Lie}(S^3)\cong\mathbb{R}^3$?

Prove that $[X, Y] = \frac{\partial^2}{\partial s \partial t} \bigg|_{0} \left[\text{exp}(sX), \text{exp}(tY)\right]$ in a Lie group

Fundamental groups of coset spaces

$PSl_n(\mathbb{C})\cong PGl_n(\mathbb{C})$?

Heisenberg Lie group, image of specific element by any representation is nilpotent

Why is the image of a faithful representation of a Lie group a Lie subgroup?

Cardinalities of set of equivalence classes of Lie groups' and algebras' representations.

First prolongation formula

The projection $G\rightarrow G/H$ is a fibre bundle with structure group $N(H)/H$?

Dimension of SO(5)

Cotangent bundle of $SO(3)$

Jordan decomposition and vector fields

The exponential map is neither injective nor surjective when $n\ge 2$?

The neighborhood $U$ of the identity generates a connected Lie group $G$. Proof check.

$\operatorname{U}(2n) \supset \frac{\operatorname{Sp}(n) \times \operatorname{Sp}(m)}{\mathbb{Z}_2}$ for what maximum of $m$?

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