Campoamor-Stursberg, RutwigCardoso, Isolda E.Ovando, Gabriela P.2023-06-182023-06-182015-10[1] A. Andrada, M. L. Barberis, I. G. Dotti, G. P. Ovando, Product structures on four dimensional solvable Lie algebras. Homology Homotopy and Applications 7, 9–37 (2005). [2] J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Mathematics, 21, 293–329 (1976). [3] V. S. Varadarajan, Lie Groups, Lie Algebras and Their Representations, Springer-Verlag New York, Graduate Texts in Mathematics, 102, (1984).0129-167X10.1142/S0129167X15500962https://hdl.handle.net/20.500.14352/24248We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h subset of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are givenengjournal articlehttp://www.worldscientific.com/doi/10.1142/S0129167X15500962http://www.worldscientific.comopen access514.7Complex structureextension problem(extended) semi-direct productsHermitian and anti-Hermitian structuresLie algebras with complex structuresGeometría diferencial1204.04 Geometría Diferencial