Undecidability of equations in free Lie algebras

Kharlampovich, Olga; Myasnikov, Alexei

doi:10.1090/tran/7579

Undecidability of equations in free Lie algebras
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Trans. Amer. Math. Soc. 371 (2019), 2987-2999 Request permission

Abstract:

In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least 3 with coefficients in an arbitrary integral domain. We also show that the ring of integers $\mathbb {Z}$ is interpretable by positive existential formulas in such free Lie algebras if the integral domain has characteristic 0.

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