On the concept of universal W-algebra

Common quadratic WN algebras are in fact particular submanifolds of naturally closed algebras of operators of Casimir kind, TrJn built from generators J of the Kas-Moody Sl(N) algebra. These submanifolds arise as a result of the Hamilton reduction and of some additional restraints of more special character, which select a closed finitely generated subalgebra (are not considered in the text). It turns out that in the limit N→∞ the structure of the Lie linear algebra is restored, and the arising new object can be naturally interpreted as a universal W-algebra