Complex structures on tangent and cotangent Lie algebras of dimension six

Abstract

This paper deals with complex structures on Lie algebras $\ct_π \hh=\hh \ltimes_π V$, where $\pi$ 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 $\pi$ 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

References in corpus (1)

• Weak mirror symmetry of Lie algebras