CONSISTENCY CONDITIONS AND REPRESENTATIONS OF A Q-DEFORMED VIRASORO ALGEBRA

We derive deformations of the Virasoro algebra in terms of "diffeomorphisms" of functions on a discretized circle. The Curtright-Zachos deformation is recovered in one case, for deformation parameter a root of unity. Consistency conditions are then derived for this algebra by introducing the so-called "braid-Jacobi" identities. All the representations are subsequently found through use of these identities. Further, it is shown that no nontrivial central term can be incorporated, since it clashes with the consistency conditions. Finally, an alternative deformation is derived which generalizes the Drinfeld deformation of the SU(1,1) subgroup to the full algebra.