Undecidability of Equations in Free Lie Algebras

Olga Kharlampovich, Alexei Myasnikov

Published 2017-08-22Version 1

In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in such free Lie algebras over a field of characteristic zero.