Stepukh V. Centralizers of elements and abelian subalgebras in Lie algebras of derivations

Centralizers of elements, maximal abelian subalgebras of Lie algebras of derivations, annihilators of sets of rational functions in Lie algebras of derivations, commutative bases of such Lie algebras and weakly semisimple polynomials are studied. A descriptions of centralizers of elements and maximal abelian subalgebras are given. Some relations among classes of commutative bases are pointed out, an approach to their constructing is obtained. A description of weakly semisimple polynomials with separated variables is given and their properties are obtained. The structure of the annihilator for a set S of rational functions is described.