LieAlgebra ++ LieAlgebra -- Take the direct sum of Lie algebras

Operator: ++

Description

Starting from simple Lie algebras, one can take direct sums and produce semi-simple ones:

i1 : g=simpleLieAlgebra("D",4);

i2 : h=simpleLieAlgebra("G",2);

i3 : g++h

o3 = 𝔡  ++ 𝔤
      4     2

o3 : LieAlgebra

i4 : directSum(g,g,h)

o4 = 𝔡  ++ 𝔡  ++ 𝔤
      4     4     2

o4 : LieAlgebra

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 $h_1\oplus h_2$.

Ways to use this method:

LieAlgebra ++ LieAlgebra -- Take the direct sum of Lie algebras

The source of this document is in LieTypes.m2:2600:0.