[GAP Forum] Help with recovering Lie brackets

[Alan Hylton]

Hi everyone,

I am brand new to GAP. I am trying to follow along the Lie algebra
documentation here:
https://www.gap-system.org/Manuals/doc/ref/chap64_mj.html

Right now I can create my Lie algebra:

gap> L := SimpleLieAlgebra( "F", 4, Rationals );

and I can my positive/negative roots and Cartan:

gap> ChevalleyBasis(L);
[ [ v.1, v.2, v.3, v.4, v.5, v.6, v.7, v.8, v.9, v.10, v.11, v.12, v.13,
v.14, v.15, v.16, v.17, v.18, v.19,
      v.20, v.21, v.22, v.23, v.24 ], [ v.25, v.26, v.27, v.28, v.29, v.30,
v.31, v.32, v.33, v.34, v.35, v.36,
      v.37, v.38, v.39, v.40, v.41, v.42, v.43, v.44, v.45, v.46, v.47,
v.48 ], [ v.49, v.50, v.51, v.52 ] ]

But I cannot figure out how to do basic computations - like [e1, e2]. There
is a function called LieBracket, and the documentation suggests that *
works, but I can't get either to work.

I would also like to see if I can return a list of non-trivial bracket
relations, or structure constants. I found there is a function called
StructureConstantsTable, but it does not seem to work with L.

I'm sorry to ask what is surely simple stuff - I just don't see it yet.

Thanks!
agh