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Question: about root decomposition in Lie algebras

Question:about root decomposition in Lie algebras

Maryry 15 Maple 2022
liealgebra decomposition
June 25 2023
2

 For the command LieAlgebras[RootSpaceDecomposition] I don't understand what the command return, I read the help and see the examples but still not understanding.

 

for example it returns:

RSD := RootSpaceDecomposition(CSA);

RSD := table([[-2, -1] = E31, [2, 1] = E13, [1, 2] = E23, [1, -1] = E12, [-1, 1] = E21, [-1, -2] = E32])

I don't understand what means [-2, -1] even they said that is the root but I know that a root is in h* so it must be only a number not a vector.
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