A two-sorted theory of nilpotent Lie algebras

Christian d'Elbée; Isabel Müller; Nicholas Ramsey; Daoud Siniora

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arXiv · 2407.12452

A two-sorted theory of nilpotent Lie algebras

Christian d'Elbée·Isabel Müller·Nicholas Ramsey·Daoud Siniora

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Abstract

We prove the existence of a model companion of the two-sorted theory of $c$-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field sort. Using a new criterion which does not rely on a stationary independence relation, we prove that if the field is NSOP$_1$, then the model companion is NSOP$_4$. We also prove that if the field is algebraically closed, then the model companion is $c$-NIP.

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BibTeX RIS

Christian d'Elbée, Isabel Müller, Nicholas Ramsey, Daoud Siniora. 2024-07-17. A two-sorted theory of nilpotent Lie algebras. https://arxiv.org/abs/2407.12452

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