  The procedure of double extension of vector spaces endowed with
non-degenerate bilinear forms allows us to introduce the class of generalized
$\mbK$-oscillator algebras over any arbitrary field $\mbK$. Starting from basic
structural properties of such algebras and the canonical forms of skew-adjoint
endomorphisms, we will proceed to classify the subclass of quadratic nilpotent
algebras and characterize those algebras in the class with quadratic dimension
2. This will enable us to recover the well-known classification of real
oscillator algebras, also known as Lorentzian algebras, given by Alberto Medina
in 1985.
