Undecidability of equations in free Lie algebras
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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.References
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Additional Information
- Olga Kharlampovich
- Affiliation: Department of Mathematics and Statistics, Hunter College, CUNY, New York, New York 10065
- MR Author ID: 191704
- Alexei Myasnikov
- Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030
- MR Author ID: 670299
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 2987-2999
- MSC (2010): Primary 03C60
- DOI: https://doi.org/10.1090/tran/7579
- MathSciNet review: 3896103