Intereting Posts

Two 2d vector angle clockwise predicate
Why Cauchy's definition of infinitesimal is not widely used?
Derivative of matrix involving trace and log
Limit involving incomplete gamma function
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
Average number of trials until drawing $k$ red balls out of a box with $m$ blue and $n$ red balls
Proof that the function $\cot(\pi z)$ is uniformly bounded on the sides of the square with vertices $\pm(N+1/2)\pm i(N+1/2),n∈ℕ$.
What's wrong with l'Hopital's rule?
Is the root of $x=\cos(x)$ a transcendental number?
$ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $
Area under parabola using geometry
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
if $\Omega=\{1,2,3,\cdots \}$ then $S_{\Omega}$ is an infinite group
Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
The prime number theorem and the nth prime

Given a Matrix Lie Group, the Lie Bracket is of the associated Lie Algebra is given by the Lie Derivative. Is this always the commutator if we start from a Matrix Lie Group?

Cheers!

- Does $e^Xe^Y = e^Ye^X$ iff $=0$ hold once we are sufficiently close to the identity of a Lie group?
- Is the exponential map ever not injective?
- Examples of Free Lie Algebra
- Exterior product generates the infinitesimal rotations — what is the geometric significance?
- Compute $ad_X$, $ad_Y$, and $ad_Z$ relative to a basis
- An short exact sequence of $\mathfrak{g}$ of which head and tail are in category $\mathcal{O}$.

- Jacobian of exponential mapping in SO3/SE3
- Examples about that $\exp(X+Y)=\exp(X) \exp(Y)$ does not imply $=0$ where $X,Y$ are $n \times n $ matrix
- Shrinking Group Actions
- Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
- Are the $C$-points of a simply connected algbraic group simply connected?
- How to derive these Lie Series formulas
- Is $SO_n({\mathbb R})$ a divisible group?
- Calculating the differential of the inverse of matrix exp?
- Complex Lie algebra $\mathfrak{g}$ is solvable implies that $\mathfrak{g}'$ is nilpotent.
- Applications of Algebra in Physics

Yes; one can prove that the Lie bracket in the Lie algebra of the general linear group is the matrix commutator. Any matrix group is a subgroup of this with corresponding subalgebra and the bracket of the subalgebra is just the restriction of the original bracket.

- showing a collection of sets contain all closed sets
- Permutation and Combination- Rowing a Boat
- What is so special about negative numbers $m$, $\mathbb{Z}$?
- Sequence of measurable functions
- Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?
- Summation of a function 2
- How do you compute negative numbers to fractional powers?
- Show that lower semicontinuous function is the supremum of an increasing sequence of continuous functions
- When is a Markov process independent-increment?
- The set of lines in $\mathbb{R}^2$ is a Möbius band?
- What is a good asymptotic for $f_n = f_{n-1}+\ln(f_{n-1})$?
- How many ways are there of coloring the vertices of a regular $n$-gon
- Given two corners of a rectangle, and an angle of rotation, is it possible to calculate the position of the other corners?
- If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP
- A construction on boolean lattices is itself a boolean lattice?