Undecidability of Equations in Free Lie Algebras

Abstract

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.

arXiv admin note: text overlap with arXiv:1606.03617