CONTACT NILPOTENT LIE ALGEBRAS

In this work we show that for n >= 1, every finite (2n + 3)dimensional contact nilpotent Lie algebra g can be obtained as a double extension of a contact nilpotent Lie algebra h of codimension 2. As a consequence, for n >= 1, every (2n + 3)-dimensional contact nilpotent Lie algebra g can be obtained from the 3-dimensional Heisenberg Lie algebra h(3), by applying a finite number of successive series of double extensions. As a byproduct, we obtain an alternative proof of the fact that a (2n + 1)-nilpotent Lie algebra g is a contact Lie algebra if and only if it is a central extension of a nilpotent symplectic Lie algebra.