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Hom-Lie algebras defined on central extensions of a given quadratic Liealgebra that in turn admit an invariant metric, are studied. It is shown howsome of these algebras are naturally equipped with other symmetric, bilinearforms that satisfy an invariant condition for their twisted multiplicationmaps. The twisted invariant bilinear forms so obtained resemble theCartan-Killing forms defined on ordinary Lie algebras. This fact allows one toreproduce on the Hom-Lie algebras hereby studied, some results that areclassically associated to the ordinary Cartan-Killing form.

Hom-Lie algebra structures on quadratic Lie algebras and twisted invariant Killing-like forms defined on them