Geometric structures on lie algebras and double extensions

Given a finite-dimensional real or complex Lie algebra g equipped with a geometric structure (i.e., either an invariant metric, a symplectic or contact structure), the aim of this work is to show that the double extension process introduced by V. Kac allows one to generate Lie algebras equipped with the same type of geometric structure. In particular, for an exact symplectic Lie algebra, through a double extension process it is possible to construct new exact symplectic Lie algebras. ©2018 Amerian Mathematial Soiety.

VIVO