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Transactions of the American Mathematical Society

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Undecidability of equations in free Lie algebras


Authors: Olga Kharlampovich and Alexei Myasnikov
Journal: Trans. Amer. Math. Soc. 371 (2019), 2987-2999
MSC (2010): Primary 03C60
DOI: https://doi.org/10.1090/tran/7579
Published electronically: October 2, 2018
MathSciNet review: 3896103
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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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Additional Information

Olga Kharlampovich
Affiliation: Department of Mathematics and Statistics, Hunter College, CUNY, New York, New York 10065

Alexei Myasnikov
Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030

DOI: https://doi.org/10.1090/tran/7579
Received by editor(s): September 1, 2017
Received by editor(s) in revised form: March 13, 2018
Published electronically: October 2, 2018
Additional Notes: The first author was supported by the PSC-CUNY award, jointly funded by The Professional Staff Congress and The City University of New York and by a grant 461171 from the Simons Foundation.
Article copyright: © Copyright 2018 American Mathematical Society