A two-sorted theory of nilpotent Lie algebras
Logic
2025-07-18 v2
Abstract
We prove the existence of a model companion of the two-sorted theory of -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, then the model companion is NSOP. We also prove that if the field is algebraically closed, then the model companion is -NIP.
Cite
@article{arxiv.2407.12452,
title = {A two-sorted theory of nilpotent Lie algebras},
author = {Christian d'Elbée and Isabel Müller and Nicholas Ramsey and Daoud Siniora},
journal= {arXiv preprint arXiv:2407.12452},
year = {2025}
}