Publication:
Extending invariant complex structures

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2015-10
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World Scientific
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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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[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).
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