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

2015/07/01 by Falcone, Giovanni, Figula, Ágota
#15A63 #17B05 #17B30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1507.00137

Abstract

We classify finite-dimensional nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO₂(\mathbb R). This enables one to enlarge the class of nilpotent Lie algebras of type n,2.

Related

• On classification of (n+5)-dimensional nilpotent n-Lie algebra of class two
• Low dimensional nilpotent n-Lie algebras
• A note on extensions of nilpotent algebras of Type 2
• Lie algebras with associative structures. Applications to the study of 2-step nilpotent Lie algebras
• Geometry of central extensions of nilpotent Lie algebras