Intereting Posts

Why $0!$ is equal to $1$?
Prove that $\Bbb R^2 – \{0\}$ is homeomorphic to $S^1 \times \Bbb R$.
Does delta distribution remain continuous with respect to quasinorm?
Division of regular tetrahedron
How can I conclude that F a continuous vector field on unit ball gives a map of degree zero?
Completion and algebraic closure commutable
Sampling $Q$ uniformly where $Q^TQ=I$
Matrix with non-negative eigenvalues (and additional assumption)
Some co-finite subsets of rational numbers
Good introductory book for Markov processes
When can we not treat differentials as fractions? And when is it perfectly OK?
Infinitely differentiable function.
We know the dimension of the Koch snowflake's perimeter, but does it have a measure?
Set of continuity points of a real function
Are Hausdorff compactifications of a Tychonoff space $X$ in one-to-one correspondence with completely regular subalgebras of $BC(X)$?

Is there a Lie Algebra $\mathfrak g$ so that the extension

$0\xrightarrow{}\mathfrak h\xrightarrow{}\mathfrak g\xrightarrow{}\mathfrak q\xrightarrow{}0$

does not split, i.e. $\mathfrak g$ is not a semi-direct product of $\mathfrak h$ and $\mathfrak q$?

As I understand it, $\mathfrak q$ should not be identifiable with a subalgebra of $\mathfrak g$, right? Since $\mathfrak h$ is already an ideal in $\mathfrak g$ as the kernel.

- k-dimension of tensor product of two modules over a k-algebra
- Is such a field element an element of a subring?
- If a group is the union of two subgroups, is one subgroup the group itself?
- Let $R$ be the set of all integers with alternative ring operations defined below. Show that $\Bbb Z$ is isomorphic to $R$.
- In $k/(XW−YZ)$, there is no GCD of $xw$ and $xy$
- $G$ is a nonabelian finite group, then $|Z(G)|\leq \frac{1}{4}|G|$

- Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
- Is there an easy way to see associativity or non-associativity from an operation's table?
- Is the product of closed subgroups in topological group closed?
- Why is the ring of matrices over a field simple?
- Does $\text{End}_R(I)=R$ always hold when $R$ is an integrally closed domain?
- Existence of Zero Divisors in $C(X,\mathbb{R})$
- A question about primary decomposition and invariant factor decomposition
- Polynomial with infinitely many zeros.
- Question about fields and quotients of polynomial rings
- Discrete valuations of the rational numbers

I guess the Heisenberg algebra will do. This is the algebra $\mathfrak{g}$ with basis $a, b, c$, and products $[a, b] = c$, $[a, c] = [b, c] = 0$. Take $\mathfrak{h} = \langle c \rangle$. Then $\mathfrak{q}$ is a two-dimensional abelian algebra, and all such object in $\mathfrak{g}$ contain $c$.

- Parabola and a line
- How to prove that $f(x)=(x-1)^2(x-2)^2(x-3)^2\cdots(x-2013)^2+2014$ is reducible?
- Continuous bounded functions in $L^1$
- Is there an alternate definition for $\{ z \in \mathbb{C} \colon \vert z \vert \leq 1 \} $.
- Smoothest function which passes through given points?
- $\lim_{n\to \infty }\cos (\pi\sqrt{n^{2}-n})$ – second battle
- Books for starting with analysis
- The space obtained by identifying the antipodal points of a circle
- Complex ($\mathbb C$) least squares derivation
- Every proper subspace of a normed vector space has empty interior
- Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
- The Galois group for the following field extension
- If a 1 meter rope is cut at two uniformly randomly chosen points, what is the average length of the smallest piece?
- Proof of matrix norm property: submultiplicativity
- Generalized Eisenstein's Criterion over Integral Domains?