On extensions of Frobenius-Kähler and Sasakian Lie algebras

Extensions of Lie algebras equipped with Sasakian or Frobenius-Kähler geometrical structures are studied. Conditions are given so that a double extension of a Sasakian Lie algebra be Sasakian again. Conditions are also given for obtaining either a Sasakian or a Frobernius-Kähler Lie algebra upon respectively extending a Frobernius-Kähler or a Sasakian Lie algebra by adjoining a derivation of the source algebra. Low-dimensional examples are included.