In the study of finite dimensional Lie algebras, the notion of double extension  plays a significant role providing an inductive construction for finite dimensional quadratic or symplectic Lie algebras in terms of a minimal  ideal and successive applications of the double extensión process. This also can be applied in the context of Lie algebras endowed with a contact structure. In this area my contibutions have been the following: provide conditions in order to a double extension of a contact Lie algebra can be a contact Lie algebra again; show that there are contact Lie algebras that cannot be expressed as a double extension of a contact Lie algebra of codimension 2; prove that every contact nilpotent Lie algebra having dimension greater than 5 can be constructed from the 3-dimensional Heisenberg Lie algebra, through a successive application of appropriate double extensions; given a finite-dimensional Lie algebra  equipped either with an invariant metric, a symplectic structure or a contact structure, to determine whether a double extension of such Lie algebra  produces a Lie algebra equipped with the same type of geometric structure.

1. Construction of finite dimensional Lie (super)algebras endowed with a geometric structure

1. Basic Mathematics
2. Applied Mathematics