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arXiv · 1406.4091

Extending invariant complex structures

Rutwig Campoamor Stursberg·Isolda E. Cardoso·Gabriela P. Ovando
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Abstract

We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h 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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Rutwig Campoamor Stursberg, Isolda E. Cardoso, Gabriela P. Ovando. 2014-06-16. Extending invariant complex structures. https://arxiv.org/abs/1406.4091

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