On nilpotent Lie algebras of derivations with large center

Let $\mathbb K$ be a field of characteristic zero and $A$ an associative commutative $\mathbb K$-algebra that is an integral domain. Denote by $R$ the quotient field of $A$ and by $W(A)=R\operatorname{Der} A$ the Lie algebra of derivations on $R$ that are products of elements of $R$ and derivations on $A$. Nilpotent Lie subalgebras of the Lie algebra $W(A)$ of rank $n$ over $R$ with the center of rank $n-1$ are studied. It is proved that such a Lie algebra $L$ is isomorphic to a subalgebra of the Lie algebra $u_n(F)$ of triangular polynomial derivations where $F$ is the field of constants for $L$.