Abstract
The (non-linearly) extended conformal algebras associated with su( N) ( W N -algebras) contain operators W ̃ k(z) of dimensions k=2,3, …, N. We show that in the N→∞ limit, the quantum (commutator) algebra of the W ̃ k(z) reduces to their classical (Poisson bracket) algebra. In particular, this proves the closure — in the usual non-linear sense — of the quantum W ∞ algebra.
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