Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic

Oksana Bezushchak; Anatoliy Petravchuk

paper

Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic

arXiv:2610.15731

Abstract

Let $F$ be a field of positive characteristic, and let $A$ be a finitely generated commutative associative $F$ -algebra. We study Lie subalgebras of $D er A$ generated by locally finite derivations. We prove that if all commutators of the generators satisfy a natural local finiteness condition, then the associative subalgebra of $E n d_{F} A$ generated by these derivations is finite-dimensional.