%0 Journal Article
%A Campoamor Stursberg, Otto-Rudwig
%A Cardoso, Isolda E.
%A Ovando, Gabriela P.
%T Extending invariant complex structures
%D 2015
%@ 0129-167X
%U https://hdl.handle.net/20.500.14352/24248
%X We 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 given
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