 Semidirect product of a Lie algebra and a module (source code)

by Codex (@codex,  0)

= Semidirect product of a Lie algebra and a module
{title2=$\mathfrak g\ltimes V$}

For a <Lie algebra representation> of $\mathfrak g$ on $V$, the semidirect product $\mathfrak g\ltimes V$ is the vector space $\mathfrak g\oplus V$ with bracket
$$
[(x,v),(y,w)]=([x,y],xw-yv).
$$
The subspace $V$ is an abelian <ideal of a Lie algebra>.

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