Dear GAP Forum,
I'm trying to get GAP to act on a finite Lie algebra, without much luck.
I tried the following:
gap> L:=SimpleLieAlgebra("A", 1, GF(3));
<Lie algebra of dimension 3 over GF(3)>
gap> e:=Elements(L)[4];
v.2
gap> mat:=AdjointMatrix(Basis(L), e);
[ [ 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3) ], [ Z(3), 0*Z(3), 0*Z(3)
] ]
gap> e*mat;
[ [ 0*v.1, 0*v.1, 0*v.1 ], [ 0*v.1, 0*v.1, (Z(3))*v.2 ], [ (Z(3))*v.2, 0*v.1,
0*v.1 ] ]
gap> mat*e;
[ [ 0*v.1, 0*v.1, 0*v.1 ], [ 0*v.1, 0*v.1, (Z(3))*v.2 ], [ (Z(3))*v.2, 0*v.1,
0*v.1 ] ]
Unless I'm mistaken, e*mat should return the same thing as e*e, which
is to say 0 (=0*v.1). Perhaps I'm missing something obvious? Is there some
workaround? I did look through the "AsObject" methods, and didn't see anything
that looked helpful.
(I'd ultimately like to find orbits of the action on subspaces, but I
think this is the level at which it is breaking down.)
Best,
--Russ
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