Intereting Posts

The structure of a Noetherian ring in which every element is an idempotent.
Are simple functions dense in $L^\infty$?
Zeta function values in terms of Bernoulli numbers.
When do the Freshman's dream product and quotient rules for differentiation hold?
Symplectic basis $(A_i,B_i)$ such that $S= $ span$(A_1,B_1,…,A_k,B_k)$ for some $k$ when $S$ is symplectic
How to convince a math teacher of this simple and obvious fact?
An arbitrary product of connected spaces is connected
Volume of $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$
Exactness of short exact sequences
Zorn's Lemma And Axiom of Choice
Roman Numbers – Conversion to decimal number
If $R$ is a local ring, is $R]$ (the ring of formal power series) also a local ring?
Solution of $\frac{d^2y}{dx^2} – \frac{H(x) y}{b} = H(-x)$
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
Equivalent of the countable axiom of choice?

I would like to ask, how to deduce a Lie group action, from infinitesimal action of its Lie algebra (the so called Lie-Palais theorem). More precisely, given a differential manifold $M$ and a Lie group $G$ with Lie algebra $\mathcal{G}$.

Suppose we have a Lie algebra homomorphism

$$\rho : \mathcal{G}\rightarrow\mathfrak{X}(M)$$

(where $\mathfrak{X}(M)$ denotes the space of vector fields of $M$).

How to deduce, from $\rho$, a smooth action

$$G\times M\rightarrow M\ ?$$

In particular, is there a nice and elementary proof of the Lie-Palais theorem?

Thanks for you help.

- Why is the image of the implicit function in the implicit function theorem not open?
- Is it possible to elementarily parametrize a circle without using trigonometric functions?
- Almost complex structures on spheres
- Smooth boundary condition implies exterior sphere condition
- Universal Definition for Pullback
- Determining the angle degree of an arc in ellipse?

- Sufficient condition for $M$ to have constant curvature
- Differential of a smooth function
- If $dF_p$ is nonsingular, then $F(p)\in$ Int$N$
- Path density between two points
- Understanding tangent vectors
- Line bundles of the circle
- Lie derivative of a vector field equals the lie bracket
- antipodal map of complex projective space
- Isoperimetric inequality, isodiametric inequality, hyperplane conjecture… what are the inequalities of this kind known or conjectured?
- Curvature of geodesic circles on surface with constant curvature

- The following groups are the same.
- Prove that if $n$ is composite, then $(n-1)! \equiv 0 \pmod n$
- Finding $\lim\limits_{x\to 0} \frac{a^x-1}{x}$ without L'Hopital and series expansion.
- Find limits $\lim_{n\to\infty}\left(2n\int_{0}^{1}\dfrac{x^n}{1+x^2}dx\right)^n$
- For every integer $n$, $15\mid n$ iff $3\mid n$ and $5\mid n$
- Reference – Riemannian Orbifolds
- completeness and closedness for a subset in a metric space
- Equivalent form of definition of manifolds.
- Unique subgroup of index 2 in a finite abelian group.
- Set of open intervals in R with rational endpoints is a basis for standard topology on R
- Arithmetic on $$: is $0 \cdot \infty = 0$ the only reasonable choice?
- Bounding the prime counting function
- Expectation value of a product of an Ito integral and a function of a Brownian motion
- check whether a convolution has compact support
- Ideal of $\mathbb{C}$ not generated by two elements