FRACTIONAL SUPERSPACE FORMULATION OF GENERALIZED SUPER-VIRASORO ALGEBRAS

We present a fractional superspace formulation of the centerless parasuper-Virasoro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by t and theta, with t a real coordinate and theta a paragrassmann variable of order M and canonical dimension 1/F. We further describe a more general structure labeled by M and F with M greater-than-or-equal-to F. The case F = 2 corresponds to the parasuper-Virasoro algebra of order M, while the case F = M leads to the fractional super-Virasoro algebra of order F. The ordinary super-Virasoro algebra is recovered at F = M = 2. The connection with q-oscillator algebras is discussed.