Complex structures on tangent and cotangent Lie algebras of dimension six

Stursberg, Rutwig Campoamor; Ovando, Gabriela P.

Complex structures on tangent and cotangent Lie algebras of dimension six

Authors

Description

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.
18 pages, extended and improved version