[GAP Forum] matrix acting on Lie algebra

[Russ Woodroofe]

	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