Algebraic structures on quasi-primary states in superconformal algebras

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The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is given. The list contains a one-parameter family of superconformal algebras with 4 supercharges that is simple for general values.
22 pages; errors corrected, terminology slightly revised, remarks added

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