Invariant filtrations of Lie algebras of Cartan type over commutative rings (Q1902252)

Let \(L\) be a filtered Lie algebra of Cartan type over a commutative ring \(R\) of characteristic \(p>3\). The elementary proof of the fact, that the natural filtration \(\{L_i\}\) of \(L\) is invariant in the case when the nilradical \(N\) of \(R\) is trivial, is given. In the general case, \(L_\infty= NL\) is an invariant ideal of \(L\). It is proved that the filtration \(\{\overline{L}_i= L_i+L_\infty\}\) is invariant.