Intereting Posts

First-order nonlinear ordinary differential equation
If $ \cos(x) \cos(2x) \cos(3x) = \frac{4}{7} $ find $ \frac{1}{\cos^2{x}}+\frac{1}{\cos^2{2x}} + \frac{1}{\cos^2{3x}} $
Using strong induction to get the AM-GM inequality for $2^n$ numbers
Why is this integral $\int_{-\infty}^{+\infty} F(f(x)) – F(x) dx = 0$?
Prove Laurent Series Expansion is Unique
What are the units of cyclotomic integers?
Connecting a $n, n$ point grid
Equality of measures on a generated $\sigma$-algebra
How to prove this polynomial inequality?
Can you equip every vector space with a Hilbert space structure?
Sum of two countably infinite sets
There exists a vector $c\in C$ with $c\cdot b=1$
Number of combinations and permutations of letters
Faithful irreducible representations of cyclic and dihedral groups over finite fields
Elliott Mendelson, Introduction to Mathematical Logic – Gen-rule and logical consequence

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!

- Showing the Lie Algebras $\mathfrak{su}(2)$ and $\mathfrak{sl}(2,\mathbb{R})$ are not isomorphic.
- Finding the basis of $\mathfrak{so}(2,2)$ (Lie-Algebra of $SO(2,2)$)
- Representations of Direct Sum of Lie Algebras
- Does the abstract Jordan decomposition agree with the usual Jordan decomposition in a semisimple Lie subalgebra of endomorphisms?
- Definition of a “root” of a Lie Algebra
- Vector bundle and principal bundle

- Differential of the inversion of Lie group
- Can somebody explain the plate trick to me?
- Representations of Direct Sum of Lie Algebras
- Do we have $(g \wedge g)^g = 0$?
- Which Lie groups have Lie algebras admitting an Ad-invariant inner product?
- Lie group structure on some topological spaces
- To what extent are the Jordan-Chevalley and Levi Decompositions compatible.
- How to determine the matrix of adjoint representation of Lie algebra?
- Spinor Mapping is Surjective
- Parabolic subgroups of $\mathrm{Sl}_n$ are the ones that stabilize some flag

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.

- Distribution for random harmonic series
- Sum : $\sum \sin \left( \frac{(2\lfloor \sqrt{kn} \rfloor +1)\pi}{2n} \right)$.
- Confused about models of ZFC and passage of book
- Functional equations leading to sine and cosine
- Probability of crossing a point in a given time window
- Deciding whether two metrics are topologically equivalent in the space $C^1()$
- Is the equation $\phi(\pi(\phi^\pi)) = 1$ true? And if so, how?
- Modules with projective dimension $n$ have not vanishing $\mathrm{Ext}^n$
- Is a uniformly continuous function vanishing at $0$ bounded by $a|x|+c$?
- Is it generally accepted that if you throw a dart at a number line you will NEVER hit a rational number?
- Is the class of cardinals totally ordered?
- Prove the following ceiling and floor identities?
- Catalan number interpretation
- How to calculate $\sum_{n=1}^\infty\frac{(-1)^n}n H_n^2$?
- Some basic book to start with modules?