Complex structures on tangent and cotangent Lie algebras of dimension six

2008/05/16 by Rutwig Campoamor-Stursberg, Rutwig Campoamor Stursberg, Stursberg, Rutwig Campoamor +2
Mathematics · #22E25. #53C15 #53C55 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:22E25. #msc:53C15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.0805.2520

18 pages, extended and improved version

openalex publication_date 2008/05/16 · arxiv created 2009/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with complex structures on Lie algebras \ct_π \hh=\hh \ltimes_π V, where π is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on \ct_π \hh for \hh a three dimensional real Lie algebra. First it was proposed the study of complex structures J satisfying the constrain J\hh=V. Whenever π is the adjoint representation this kind of complex structures are associated to non singular derivations of \hh. This fact derives different kind of applications. Finally an approach to the pseudo Kähler geometry was done.

Citations

• Complex structures on nilpotent Lie algebras
• Curvatures of left invariant metrics on lie groups
• Weak mirror symmetry of Lie algebras
• Generalized Complex Geometry

Related

• Symplectic, product and complex structures on 3-Lie algebras
• Complex and Kahler structures on hom-Lie algebras
• Classification of integrable complex structures on 6-dimensional product Lie algebras
• Complex structures on nilpotent Lie algebras
• Complex Product Structures on Lie Algebras