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

Abstract

We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO2(ℝR). This is the first step to extend the class of nilpotent Lie algebras of type {n,2} to solvable Lie algebras in which has codimension one.