The action of a compact Lie group on nilpotent Lie algebras of type {n,2}

We classify finite-dimensional nilpotent Lie algebras with $2$-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to $S{O}_2(\mathbb{R})$. This enables one to enlarge the class of nilpotent Lie algebras of type {n,2}.