Dear R.N. and GAP-forum, The factor 2 is explained by the fact that the operation * on a Lie algebra in GAP is already the Lie bracket: > B1:=M(A1*A2-A2*A1); So this should read M(A1*A2), and then > B2:=M(A1)*M(A2)-M(A2)*M(A1); will be zero. Best wishes, Jan