  A Lie algebra is said to be metric if it admits a symmetric invariant and
nondegenerate bilinear form. The harmonic oscillator algebra, which arises in
the quantum mechanical description of a harmonic oscillator, is the smallest
solvable nonabelian metric example. This algebra is the first step of a
countable series of solvable Lie algebras which support invariant Lorentzian
forms. Generalizing this situation, in this paper we arrive to the oscillator
Lie K-algebras as double extensions of metric spaces. The aim of this paper is
to present some structural features, invariant metrics and derivations of this
class of algebras and to explore their possibilities of being extended to mixed
metric Lie algebras.
