# Tag Info

## Hot answers tagged lie-groups

Accepted

• 10.9k
1 vote

### The action of $SL(n,\Bbb{R})$ on the tangent space of $SL(n,\Bbb{R})/SO(n)$.

You are making certain (very interesting !) mistakes. This is not quite my field, so I apologize if I say something imprecise. The overall issue is the question of "the tangent space of $P$ at $p$...
1 vote
Accepted

### Conjugacy action of $SO(2m)$ on $O(2m)/U(m)$

As I suggested in a hint, it is useful to consider first the case $n=2$. Then there are exactly two order 4 rotations in the plane, namely, $J_1$ and $-J_1$ (rotations by $\pi/2$ and $-\pi/2$). They ...
• 101k
1 vote
Accepted

### Geometric interpretation and upper bounds on Euclidean distance in Lie algebra of SO(3)

The 2-norm on the Lie algebra of $SO(3)$ (the space of skew-symmetric $3\times 3$ matrices) is, up to a constant multiple, the Frobenius norm, i.e. with this norm $SO(3)$ is a Riemannian manifold. I ...
• 101k
1 vote
Accepted

### Question on the proof of Engel's Theorem step 1 in book Introduction to Lie Algebras

Those are two separate claims both of which they prove later. In fact they are simply stating what they plan to show in the proof. They show that $\tilde{A} = A \oplus \mathrm{Span}\{y\}$ is a larger ...
• 4,721
1 vote

### Motivation for Studying Nilpotent and Solvable Lie Algebras

I know it's been over 7 years, but I'll post this excerpt from the book "Emergence of the theory of Lie groups" by Thomas Hawkins because I find the accepted answer quite dismissive of the ...
• 1,313

Only top scored, non community-wiki answers of a minimum length are eligible