On nilpotent Lie algebras of derivations with large center

Abstract

Let K be a field of characteristic zero and A an associative commutative K-algebra that is an integral domain. Denote by R the quotient field of A and by W(A)=RDerA 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 un(F) of triangular polynomial derivations where F is the field of constants for L.