Five-dimensional paracontact Lie algebras

We consider odd-dimensional Lie algebras gequipped with a paracontact metric structure. In the case of non-trivial center, paracontact Lie algebras are obtained as central extensions of almost paraKähler Lie algebras. As such, they are necessarily K-paracontact, and a complete classification is given in dimension five, also specifying the paraSasakian examples. Thus, paracontact, not K-paracontact structures can only occur among Lie algebras with trivial center. Starting from the classification of five-dimensional contact Lie algebras given in [17], examples with trivial center, both K-paracontact and not, are explicitly discussed and classified.