Dear Dima, Here the problem is that your Lie algebra is not semisimple; you would need to take its derived subalgebra:
D:= LieDerivedSubalgebra(ll); But then it returns fail as well, as the Cartan subalgebra is not split over the rationals (and as far as I am aware GAP does not have methods to factor polynomials over extensions): h:= Basis( CartanSubalgebra(D) )[1];; ad:= AdjointMatrix( Basis(ll), h );; gap> MinimalPolynomial(Rationals,ad); x^3-7*x Best wishes, Willem Dear all, is the following a bug, or a feature? gap> aa; [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 2, 0, 0 ], [ 1, 1, 0, 0 ], [ 0, 0, 0, 2 ], [ 0, 0, 1, 1 ] ], [ [ -2, 0, -4, -4 ], [ 0, 0, 0, 4 ], [ 1, 1, 0, 2 ], [ 0, -1, 0, -2 ] ], [ [ 0, 0, 0, 8 ], [ -2, 0, -4, 0 ], [ 0, -2, 0, -4 ], [ 1, 0, 0, 0 ] ] ] gap> ll:=LieAlgebra(Rationals,aa); <Lie algebra over Rationals, with 4 generators> gap> RootSystem(ll); fail gap> (In fact, I know that this algebra is isomorphic to gl(2,C), and I would like to find its representation in M_2(C)) Thanks, Dmitrii _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
