List questions from lie-groups

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Prove that the map $\phi:S^3\times S^3\to{\bf GL}(4,\Bbb R)$ defined via quaternions as$\phi(p,q)(v)=pvq^{-1}$ has image ${\bf SO}(4)$

Published on 17 Apr 2026 - 8:07

2.1k

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Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?

Published on 15 Apr 2026 - 16:06

291

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Cohomology ring of $U(n)$

Published on 13 Apr 2026 - 23:29

5.5k

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Getting started with Lie Groups

Published on 13 Apr 2026 - 3:35

440

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describing the geometry of a Lie group

Published on 17 Apr 2026 - 7:40

665

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decomposition of Haar measure and Fubini theorem

Published on 14 Apr 2026 - 5:51

553

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Matrix Exponential equality

Published on 16 Apr 2026 - 23:08

118

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Commutator of Pauli-Lubanski operator

Published on 11 Apr 2026 - 7:48

114

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action of $O(n,\mathbb{R})$ on ${S}^{n-1}$

Published on 15 Apr 2026 - 8:07

796

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Does non-commuting $\mathfrak{g}$ imply non-abelian $G$?

Published on 15 Apr 2026 - 10:37

107

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Supremum over unitary group action

Published on 09 Apr 2026 - 5:42

1.9k

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What is the main use of Lie brackets in the Lie algebra of a Lie group?

Published on 14 Apr 2026 - 7:06

743

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Centre of a connected Lie group.

Published on 12 Apr 2026 - 5:42

2.2k

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How that the Lie algebra of the normalizer of a Lie group equal the normalizer of the Lie algebra

Published on 13 Apr 2026 - 19:44

198

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$\pi_2(G)$ for $G$ a Lie group.

Published on 15 Apr 2026 - 14:49

List Question

Prove that the map $\phi:S^3\times S^3\to{\bf GL}(4,\Bbb R)$ defined via quaternions as$\phi(p,q)(v)=pvq^{-1}$ has image ${\bf SO}(4)$

Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?

Cohomology ring of $U(n)$

Getting started with Lie Groups

describing the geometry of a Lie group

decomposition of Haar measure and Fubini theorem

Matrix Exponential equality

Commutator of Pauli-Lubanski operator

action of $O(n,\mathbb{R})$ on ${S}^{n-1}$

Does non-commuting $\mathfrak{g}$ imply non-abelian $G$?

Supremum over unitary group action

What is the main use of Lie brackets in the Lie algebra of a Lie group?

Centre of a connected Lie group.

How that the Lie algebra of the normalizer of a Lie group equal the normalizer of the Lie algebra

$\pi_2(G)$ for $G$ a Lie group.

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