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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 0129167X

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

http://www.worldscientific.com  Publisher 
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 nondegenerate, 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) semidirect products; Hermitian and antiHermitian 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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