W-algebras of negative rank

Recently it has been discovered that the W-algebras (orbifold of) WDn can be defined even for negative integers n by an analytic continuation of their coupling constants. In this letter we shall argue that also the algebras WA−n−1 can be defined and are finitely generated. In addition, we show that a surprising connection exists between already known W-algebras, for example between the CP(k)-models and the -cosets of the generalized Polyakov-Bershadsky-algebras.