Complex structures on tangent and cotangent Lie algebras of dimension six

Details Complex structures on tangent and cotangent Lie algebras of dimension six Complex structures on tangent and cotangent Lie algebras of dimension six

2008-05-16

arxiv.org/abs/0805.2520v2

Mathematics

Differential Geometry

18 pages, extended and improved version

Scientific paper

This paper deals with complex structures on Lie algebras $\ct_{\pi} \hh=\hh \ltimes_{\pi} V$, where $\pi$ is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on $\ct_{\pi} \hh$ 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 K\"ahler geometry was done.

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