Abstract

A theoretical framework in which to study the Jacobi identities on the commulators of W-algebra fields is established. W-algebras containing various specified combinations of fields of spin up to 8 are classified and constructed. In the cases studied, we show that there are closed W-algebraic structures, valid for all values of the central charge c, only for those field contents corresponding to the exponents of finite-dimensional semi-simple algebras.

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