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BONN-HE-90-05 July 1990 W-Algebras with Two and Three Generators

We construct all W-algebras of chiral fields which in addition to the energy-momentum density have a single generator of conformal dimension up to 8. Some of them were unexpected, which indicates that present conjectures concerning the classification of conformally invariant quantum field theories in two dimensions are rather incomplete. We also explicitly construct the WA3-algebra with generators of dimensions 2, 3, 4.