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A two-sorted theory of nilpotent Lie algebras

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arxiv 2407.12452 v2 pith:NIIC546V submitted 2024-07-17 math.LO

Christian d'Elbée , Isabel Müller , Nicholas Ramsey , Daoud Siniora This is my paper · ORCID
classification math.LO
keywords fieldcompanionmodelprovetheoryalgebrasnilpotentnsop
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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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  1. On n-dependent groups and fields III. Multilinear forms and invariant connected components

    math.LO 2024-12 accept novelty 8.0 of 10

    Over NIP fields, infinite dimensional alternating n-linear spaces are strictly n-dependent and NSOP1, proved via a new composition lemma for NIP relations and connected-component analysis.

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