 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $A$ be the two-dimensional affine <Lie algebra> with <basis> $u,v$ and bracket $[u,v]=v$, and put
$$
\boxed{L=\mathfrak{sl}_2(\mathbb C)\oplus A.}
$$
Both factors have zero centre, so $Z(L)=0$. The line $\mathbb Cv$ in the second factor is an ideal, making $L$ <pre-supersoluble Lie algebra>[PSS]. But its quotient onto the nonabelian simple algebra $\mathfrak{sl}_2$ is not soluble. A quotient of a soluble algebra would be soluble, so $L$ is not soluble.

 Back to article page