A TWO-SORTED THEORY OF NILPOTENT LIE ALGEBRAS

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.