New N=1 Extended Superconformal Algebras with Two and Three Generators

In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a nonexplicitly covariant approach we compute all SW algebras with one generator of dimension up to 7 in addition to the super Virasoro field. In complete analogy to W algebras with two generators, most results can be classified using the representation theory of the super Virasoro algebra. Furthermore, we find that the algebra can be realized as a subalgebra of at . We also construct some new SW algebras with three generators, namely , and .