Starting from simple Lie algebras, one can take direct sums and produce semi-simple ones:
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Note that this is external direct sum, so if $g_i$ is a sub-Lie algebra of $h_i$, $i=1,2$, then $g_1\oplus g_2$ is a sub-Lie algebra of $h_1\oplus h_2$.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/LieTypes.m2:2600:0.