Undecidability of Equations in Free Lie Algebras
classification
🧮 math.LO
math.RA
keywords
algebrasfreeequationsfieldundecidabilityarbitrarycharacteristicexistential
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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.
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