Thank you! This is exactly what I needed! Best, agh
On Mon, Apr 26, 2021 at 3:20 PM Willem Adriaan De Graaf < willem.degr...@unitn.it> wrote: > 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
