CLASSIFICATION OF STRUCTURE CONSTANTS FOR W-ALGEBRAS FROM HIGHEST WEIGHTS

We show that the structure constants of W-algebras can be grouped acco rding to the lowest (bosonic) spin (s) of the algebra. The structure c onstants in each group are described by a unique formula, depending on a functional parameter h (c) that is characteristic for each algebra. As examples we give the structure constants C-33(4) and C-44(4) for t he algebras of type W (2, 3, 4,...) (that include the WA(n-1) algebras ) and the structure constant C-44(4) for the algebras of type W (2, 4, ...), especially for all the algebras WD(n), WB (0, n), WB(n) and WC(n ). It also includes the bosonic projection of the super-Virasoro algeb ra and an as yet unexplained algebra of type W (2, 4, 6) found previou sly.