Question

How to show that for every element $g$ in a Lie group, the curve $\gamma(t) = g\gamma_v(t)$ is an integral curve such that $\gamma(0) = g$?

score 716 · Answer 1 · 2026-04-16 09:44:18

716

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How to show that for every element $g$ in a Lie group, the curve $\gamma(t) = g\gamma_v(t)$ is an integral curve such that $\gamma(0) = g$?

Published on 16 Apr 2026 - 9:44

score 764 · Answer 2 · 2026-04-11 03:23:57

764

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High Dimensional Rotation Matrices As Product of In-Plane Rotations

Published on 11 Apr 2026 - 3:23

score 353 · Answer 3 · 2026-04-15 13:10:00

353

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$5$ dimensional space over $\mathbb{R}$

Published on 15 Apr 2026 - 13:10

score 520 · Answer 4 · 2026-04-14 04:32:45

520

Views

Explicit homotopy equivalence of homogeneous spaces $O(2n)/U(n)$ and $GL(2n,\mathbb{R})/GL(n,\mathbb{C})$

Published on 14 Apr 2026 - 4:32

score 3k · Answer 5 · 2026-04-15 04:17:54

3k

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why is $S^2$ not a Lie group?

Published on 15 Apr 2026 - 4:17

score 2.6k · Answer 6 · 2026-04-10 12:31:33

2.6k

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What really is a path-ordered exponential?

Published on 10 Apr 2026 - 12:31

score 240 · Answer 7 · 2026-04-14 07:16:24

240

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homomorphism between smooth algebraic groups of the same dimension

Published on 14 Apr 2026 - 7:16

score 1.8k · Answer 8 · 2026-04-11 19:25:55

1.8k

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Why represent a complex number $a+ib$ as $[\begin{smallmatrix}a & -b\\ b & \hphantom{-}a\end{smallmatrix}]$?

Published on 11 Apr 2026 - 19:25

score 98 · Answer 9 · 2026-04-13 19:13:08

98

Views

Irreducible unitary representation of a solvable lie group

Published on 13 Apr 2026 - 19:13

score 175 · Answer 10 · 2026-04-15 21:12:16

175

Views

Irreducible unitary representations of $ \Bbb{R}^{2} \rtimes_{\alpha} \Bbb{R} $.

Published on 15 Apr 2026 - 21:12

score 336 · Answer 11 · 2026-04-14 13:58:50

336

Views

Connected matrix Lie group

Published on 14 Apr 2026 - 13:58

score 556 · Answer 12 · 2026-04-23 16:34:27

556

Views

Weights in the Dynkin Basis and Eigenvalues of the Cartan Generators for SU(3)?

Published on 23 Apr 2026 - 16:34

score 195 · Answer 13 · 2026-04-14 02:46:16

195

Views

Lie Groups and Matrices

Published on 14 Apr 2026 - 2:46

score 1.7k · Answer 14 · 2026-04-15 12:37:22

1.7k

Views

Derivative of exponential maps in Lie group $G$ and the adjoint operator on its Lie algebra

Published on 15 Apr 2026 - 12:37

score 243 · Answer 15 · 2026-04-23 16:24:54

243

Views

Why does a simple coroot $\alpha^{(i)}$ correspond to a Cartan subalgebra element $H^i$?

Published on 23 Apr 2026 - 16:24

List Question

How to show that for every element $g$ in a Lie group, the curve $\gamma(t) = g\gamma_v(t)$ is an integral curve such that $\gamma(0) = g$?

High Dimensional Rotation Matrices As Product of In-Plane Rotations

$5$ dimensional space over $\mathbb{R}$

Explicit homotopy equivalence of homogeneous spaces $O(2n)/U(n)$ and $GL(2n,\mathbb{R})/GL(n,\mathbb{C})$

why is $S^2$ not a Lie group?

What really is a path-ordered exponential?

homomorphism between smooth algebraic groups of the same dimension

Why represent a complex number $a+ib$ as $[\begin{smallmatrix}a & -b\\ b & \hphantom{-}a\end{smallmatrix}]$?

Irreducible unitary representation of a solvable lie group

Irreducible unitary representations of $ \Bbb{R}^{2} \rtimes_{\alpha} \Bbb{R} $.

Connected matrix Lie group

Weights in the Dynkin Basis and Eigenvalues of the Cartan Generators for SU(3)?

Lie Groups and Matrices

Derivative of exponential maps in Lie group $G$ and the adjoint operator on its Lie algebra

Why does a simple coroot $\alpha^{(i)}$ correspond to a Cartan subalgebra element $H^i$?

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