Dear Alan, You can use * to multiply elements of a Lie algebra. In the example you mention:
gap> L:= SimpleLieAlgebra( "F", 4, Rationals ); <Lie algebra of dimension 52 over Rationals> gap> c:= ChevalleyBasis(L);; gap> c[1][1]*c[1][2]; 0*v.1 gap> c[1][1]*c[1][3]; (-1)*v.5 StructureConstantsTable is applied to a basis of L: gap> T:= StructureConstantsTable( Basis(L) );; gap> T[1][3]; [ [ 5 ], [ -1 ] ] The latter means that e1*e3 is equal to -e5 (where e1,e2,... denote the standard basis vectors). Best wishes, Willem On Sun, 25 Apr 2021 at 19:38, Alan Hylton <agh...@lehigh.edu> wrote: > 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 > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
