Question

Show that $ \exp \left(\mathfrak{sl}(2,R)\right)$ is the set of all matrices with positive trace $\geq -2$

score 1.3k · Answer 1 · 2026-04-15 13:04:06

1.3k

Views

Show that $ \exp \left(\mathfrak{sl}(2,R)\right)$ is the set of all matrices with positive trace $\geq -2$

Published on 15 Apr 2026 - 13:04

score 955 · Answer 2 · 2026-04-14 03:11:00

955

Views

Lie bracket of a semidirect product

Published on 14 Apr 2026 - 3:11

score 2.4k · Answer 3 · 2026-04-16 14:39:58

2.4k

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Finding the basis of $\mathfrak{so}(2,2)$ (Lie-Algebra of $SO(2,2)$)

Published on 16 Apr 2026 - 14:39

score 1.7k · Answer 4 · 2026-04-13 11:43:36

1.7k

Views

Proof of the Isomorphism between: $SL(2,\mathbb R) \times SL(2, \mathbb R) \cong SO^+(2,2)$

Published on 13 Apr 2026 - 11:43

score 255 · Answer 5 · 2026-04-15 10:34:50

255

Views

Lie Algebra Homomorphisms for Lie Subgroups

Published on 15 Apr 2026 - 10:34

score 225 · Answer 6 · 2026-03-29 05:35:06

225

Views

Relation of $G$-invariants and $g$ -invariants.

Published on 29 Mar 2026 - 5:35

score 259 · Answer 7 · 2026-04-13 01:26:47

259

Views

What is the relation between the usual topology of $S^1$ and its subspace topology in Homeo$(S^{n+1})$?

Published on 13 Apr 2026 - 1:26

score 224 · Answer 8 · 2026-04-12 10:03:53

224

Views

When are stabilizers of the coadjoint action equal?

Published on 12 Apr 2026 - 10:03

score 185 · Answer 9 · 2026-04-13 17:28:46

185

Views

Cartan subalgebras and Jordan Normal form

Published on 13 Apr 2026 - 17:28

score 288 · Answer 10 · 2026-04-15 09:24:44

288

Views

Is a finite volume Lie group compact?

Published on 15 Apr 2026 - 9:24

score 832 · Answer 11 · 2026-04-12 20:23:53

832

Views

Lie Algebra of $\mathrm{SO}(2)$ and $\mathrm{O}(2)$ are the SAME - why?

Published on 12 Apr 2026 - 20:23

score 117 · Answer 12 · 2026-04-12 01:35:56

117

Views

Understanding rotations of $\mathbb{R}^4$ and pairs of quaternions, showing a rotation is a product of reflections in hyperplanes

Published on 12 Apr 2026 - 1:35

score 43 · Answer 13 · 2026-04-17 13:36:44

43

Views

Check that $u_4\bar{u_3}u_2\bar{u_1}=i$ and $\bar{u_1}u_2\bar{u_3}u_4=1$ so the product of the four reflections is indeed $q \to iq$

Published on 17 Apr 2026 - 13:36

score 435 · Answer 14 · 2026-04-17 05:17:37

435

Views

On lifting an action of $G$ on $X$ to an action of $G'$ on $\tilde{X}$.

Published on 17 Apr 2026 - 5:17

score 216 · Answer 15 · 2026-03-25 20:36:07

216

Views

Examples of quotient manifolds which are not locally trivial fibrations?

Published on 25 Mar 2026 - 20:36

List Question

Show that $ \exp \left(\mathfrak{sl}(2,R)\right)$ is the set of all matrices with positive trace $\geq -2$

Lie bracket of a semidirect product

Finding the basis of $\mathfrak{so}(2,2)$ (Lie-Algebra of $SO(2,2)$)

Proof of the Isomorphism between: $SL(2,\mathbb R) \times SL(2, \mathbb R) \cong SO^+(2,2)$

Lie Algebra Homomorphisms for Lie Subgroups

Relation of $G$-invariants and $g$ -invariants.

What is the relation between the usual topology of $S^1$ and its subspace topology in Homeo$(S^{n+1})$?

When are stabilizers of the coadjoint action equal?

Cartan subalgebras and Jordan Normal form

Is a finite volume Lie group compact?

Lie Algebra of $\mathrm{SO}(2)$ and $\mathrm{O}(2)$ are the SAME - why?

Understanding rotations of $\mathbb{R}^4$ and pairs of quaternions, showing a rotation is a product of reflections in hyperplanes

Check that $u_4\bar{u_3}u_2\bar{u_1}=i$ and $\bar{u_1}u_2\bar{u_3}u_4=1$ so the product of the four reflections is indeed $q \to iq$

On lifting an action of $G$ on $X$ to an action of $G'$ on $\tilde{X}$.

Examples of quotient manifolds which are not locally trivial fibrations?

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