  One of the four well-known series of simple Lie algebras of Cartan type is
the series of Lie algebras of Special type, which are divergence-free Lie
algebras associated with polynomial algebras and the operators of taking
partial derivatives, connected with volume-preserving diffeomorphisms. In this
paper, we determine the structure space of the divergence-free Lie algebras
associated with pairs of a commutative associative algebra with an identity
element and its finite-dimensional commutative locally-finite derivation
subalgebra such that the commutative associative algebra is derivation-simple
with respect to the derivation subalgebra.
