Uncountably many non-isomorphic nilpotent real \(n\)-Lie algebras

Abstract

There are an uncountable number of non-isomorphic nilpotent real Lie algebras for every dimension greater than or equal to 7. We extend an old technique, which applies to Lie algebras of dimension greater than or equal to 10, to find corresponding results for \(n\)-Lie algebras.  In particular, for \(n \ge 6\), there are an uncountable number of non-isomorphic nilpotent real \(n\)-Lie algebras of dimension \(n+4\).