ABSTRACT
Finally, let us quote the important work of Bais eta!. [3,4], who used "third order" generalizations of Sugawara [3] and G.K.O. [4] constructions (which are of "second order") for constructing an explicit realization of the V" generators of Zam. It is now recognized that Zam is a particular case of the so-called extended algebras, appearing in t\vodimensional conformal field theories, and realized in the same \vay as operator algebras. However, it must be said that up to now, very little is known on the representation theory of such algebras. The Zamolodchikov algebra and its various generalizations are also known under the name of W -algebras.
