  The fractional supersymmetry chiral algebras in two-dimensional conformal
field theory are extended Virasoro algebras with fractional spin currents. We
show that associativity and closure of these algebras determines their
structure constants in the case that the Virasoro algebra is extended by
precisely one current. We compute the structure constants of these algebras
explicitly and we show that correlators of the currents satisfy non-Abelian
braiding relations.
