On parasasakian structures on five-dimensional Lie algebras

Para-Sasakian structures on five-dimensional contact Lie algebras $\mathfrak{g}$ with nonzero center are considered. Such Lie algebras are central extensions of the four-dimensional para-Kähler Lie algebras $(\mathfrak{h},\omega)$. In this paper, a classification of five-dimensional para-Sasakian Lie algebras with a nontrivial center is proposed, based on the classification of para-Kähler structures $J$ on symplectic Lie algebras $(\mathfrak{h},\omega)$.