Analysis shows that derivations enable extensions of Lie algebras, indicating new algebraic structures may emerge.
Extensions of Lie algebras equipped with Sasakian or Frobenius-Käahler geometric 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 Frobenius-Käahler Lie algebra upon respectively extending a Frobenius-Käahler or a Sasakian Lie algebra by adjoining a derivation of the source algebra. Low-dimensional examples are included.
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Rodríguez-Vallarte et al. (2025) studied this question.
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