Matrix Lie Groups as 4-Dimensional Hypercomplex Manifolds with Hermitian-Norden metrics

2019/03/21 by Manev, Hristo
#22E15 #22E30 #22E60 #53C15 #53C50 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.08971

Abstract

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant hypercomplex structures and the explicit matrix representation of their Lie groups. There are constructed examples of the considered structure of different types on some known Lie groups.

Related

• Lie groups of dimension 4 and almost hypercomplex manifolds with Hermitian-Norden metrics
• Almost hypercomplex manifolds with Hermitian-Norden metrics and 4-dimensional indecomposable real Lie algebras depending on two parameters
• Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure
• Homogeneous Hypercomplex Structures and the Joyce's Construction
• Hypercomplex structures on special linear groups