Abstract
This paper deals with left invariant complex structures on simply connected Lie groups, the Lie algebra of which is of the type Th D hE V, where is either the adjoint or the coadjoint representation. The main topic is the existence question of complex structures on Th for h a three dimensional real Lie algebra. First it was proposed the study of complex structures J satisfying the constraint Jh D V. Whenever is the adjoint representation this kind of complex structures are associated to non-singular derivations of h. This fact allows different kinds of applications.
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