There is a German article titled:"die adjungierten darstellungen der Chevalley-gruppen" by G.Hiss, in which submodule of FG-module of a lie algebra $L$ will be determined. My question backs to this matter that how we can check irreducibility of classical simple lie algebras over GF(2) through that paper? i WANT TO check that how we can find out a classical lie algebra like D_4 and E_6 ARE irreducible?