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Extending invariant complex structures

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Campoamor Stursberg, Otto Ruttwig and Cardoso, Isolda E. and Ovando, Gabriela P. (2015) Extending invariant complex structures. International Journal of Mathematics, 26 (11). ISSN 0129-167X

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Official URL: http://www.worldscientific.com/doi/10.1142/S0129167X15500962


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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 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


Item Type:Article
Uncontrolled Keywords:Complex structure; extension problem; (extended) semi-direct products; Hermitian and anti-Hermitian structures; Lie algebras with complex structures
Subjects:Sciences > Mathematics > Differential geometry
ID Code:34498
Deposited On:01 Dec 2015 08:44
Last Modified:12 Dec 2018 15:12

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