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

TL;DR

This paper classifies certain nilpotent Lie algebras with 2-dimensional centers that admit automorphisms from the group SO(2), expanding the known classes of such algebras.

Contribution

It provides a classification of nilpotent Lie algebras of type {n,2} with specific automorphism group actions, extending previous classifications.

Findings

Classification of nilpotent Lie algebras with 2-dimensional central commutator ideals

Identification of automorphism groups isomorphic to SO(2)

Expansion of known classes of nilpotent Lie algebras of type {n,2}

Abstract

We classify finite-dimensional nilpotent Lie algebras with $2$-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to $SO_2(\mathbb R)$. This enables one to enlarge the class of nilpotent Lie algebras of type {n,2}.