Submission date: 17 July 2024

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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Full text arXiv 2407.12452: pdf, ps.