k-dimensional central extension of Lie algebras

Question

Does the phrase "a k-dimensional central extension of the Lie algebra L" mean "a central extension of L by a k-dimensional Lie algebra"?

I cannot find any textbook which mentions to that phrase.

Many thanks for considering my stupid question!

Answer 1

Yes, it does see this for more understanding

This 1 (Schottenloher, M.: Central Extensions of Lie Algebras and Bargmann’s Theorem. Lect. Notes Phys. 759, 63-73 (2008))

This 2 (Characteristically nilpotent Lie algebras: a survey, by J. M. Ancochea and R. Campoamor)

This simple for physics (Central extension and physics, by G.M. Tuynman and W.A.J.J. Wiegerinck)