CONICET | Buscador de Institutos y Recursos Humanos

We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group $H_{2n + 1}$. Furthermore, we classify Sasakian Lie algebras of dimension 5 and determine which of them carry a Sasakian alpha-Einstein structure. We show that a 5-dimensional solvable Lie group with a left-invariant Sasakian structure and which admits a compact quotient by a discrete subgroup is isomorphic to either H_5 or a semidirect product $R ltimes (H_3 imes R)$. In particular, the compact quotient is an $S^1$-bundle over a 4-dimensional K"ahler solvmanifold.