Extended conformal algebras generated by a multiplet of primary fields

Abstract

Extended conformal algebras generated by a single multiplet of primary fields of integer or half-integer spin are studied. Closed W-algebraic structures are obtained for a finite set of values of the central charge. For odd spin a series of algebras with SO(3) symmetry is found. They are present in the (1, q) Virasoro minimal models. A free field construction for these algebras is discussed.