Question

$\operatorname{U}(4n) \supset \frac{\operatorname{Sp}(n) \times \operatorname{Sp}(m)}{\mathbb{Z}_2}$ for some maximum of $m$?

score 97 · Answer 1 · 2026-03-27 21:20:30

97

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$\operatorname{U}(4n) \supset \frac{\operatorname{Sp}(n) \times \operatorname{Sp}(m)}{\mathbb{Z}_2}$ for some maximum of $m$?

Published on 27 Mar 2026 - 21:20

score 602 · Answer 2 · 2020-07-14 16:03:22

602

Views

Explicit homomorphism from $SL_2(\mathbb{R})$ to $SO(2,1;\mathbb{R})$

Published on 14 Jul 2020 - 16:03

score 124 · Answer 3 · 2020-07-14 22:48:22

124

Views

A differential $d\rho$ of a Lie homomorphism $\rho:G\to H$ commutes with the Lie bracket. Some clarification.

Published on 14 Jul 2020 - 22:48

score 51 · Answer 4 · 2020-07-15 08:28:55

51

Views

Question about Thm 3.4.2 in Brian Hall's book in Lie Algebras

Published on 15 Jul 2020 - 8:28

score 358 · Answer 5 · 2020-07-15 10:09:26

358

Views

$[X,Y]=0 \implies \exp(X+Y)=\exp(X)\exp(Y)$

Published on 15 Jul 2020 - 10:09

score 398 · Answer 6 · 2020-07-15 13:36:56

398

Views

Shortest proof of Ado's theorem for real Lie algebras?

Published on 15 Jul 2020 - 13:36

score 496 · Answer 7 · 2026-03-30 13:37:24

496

Views

$H$ normal iff $Lie(H)$ is an ideal.

Published on 30 Mar 2026 - 13:37

score 112 · Answer 8 · 2020-07-16 08:38:40

112

Views

2-dimensional regular submanifold of $GL(2, \Bbb R)$

Published on 16 Jul 2020 - 8:38

score 16 · Answer 9 · 2020-07-16 13:45:17

16

Views

$\mathfrak{h}\subsetneq \operatorname{Lie}(\operatorname{exp}(h))$ possible?

Published on 16 Jul 2020 - 13:45

score 654 · Answer 10 · 2020-07-17 11:26:37

654

Views

Diffeomorphism theorem for Lie Groups?

Published on 17 Jul 2020 - 11:26

score 906 · Answer 11 · 2020-07-17 23:22:45

906

Views

Exponential map to simply connected abelian Lie group is an isomorphism.

Published on 17 Jul 2020 - 23:22

score 65 · Answer 12 · 2020-07-18 13:01:02

65

Views

Find the complexification of a Lie Algebra

Published on 18 Jul 2020 - 13:01

score 453 · Answer 13 · 2026-03-26 06:25:31

453

Views

Comparison between SO(n) and Spin(n) representation theory

Published on 26 Mar 2026 - 6:25

score 403 · Answer 14 · 2020-07-19 01:07:52

403

Views

Is the Lie algebra morphism induced by injective/surjective Lie group morphism also injective/surjective?

Published on 19 Jul 2020 - 1:07

score 287 · Answer 15 · 2026-03-27 21:18:06

287

Views

Open subgroups of $Gl_n$ which are not closed.

Published on 27 Mar 2026 - 21:18

List Question

$\operatorname{U}(4n) \supset \frac{\operatorname{Sp}(n) \times \operatorname{Sp}(m)}{\mathbb{Z}_2}$ for some maximum of $m$?

Explicit homomorphism from $SL_2(\mathbb{R})$ to $SO(2,1;\mathbb{R})$

A differential $d\rho$ of a Lie homomorphism $\rho:G\to H$ commutes with the Lie bracket. Some clarification.

Question about Thm 3.4.2 in Brian Hall's book in Lie Algebras

$[X,Y]=0 \implies \exp(X+Y)=\exp(X)\exp(Y)$

Shortest proof of Ado's theorem for real Lie algebras?

$H$ normal iff $Lie(H)$ is an ideal.

2-dimensional regular submanifold of $GL(2, \Bbb R)$

$\mathfrak{h}\subsetneq \operatorname{Lie}(\operatorname{exp}(h))$ possible?

Diffeomorphism theorem for Lie Groups?

Exponential map to simply connected abelian Lie group is an isomorphism.

Find the complexification of a Lie Algebra

Comparison between SO(n) and Spin(n) representation theory

Is the Lie algebra morphism induced by injective/surjective Lie group morphism also injective/surjective?

Open subgroups of $Gl_n$ which are not closed.

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