Fractional Virasoro algebras

We show that it is possible to construct a Virasoro algebra as a central extension of the fractional Witt algebra generated by non-local operators of the form, where a ε R. The Virasoro algebra is explicitly of the form, where Am;n(s) is a specific meromorphic function c is the central charge (not necessarily a constant), Za is in the center of the alge-bra and h(n) obeys a recursion relation related to the coefficients Am;n. In fact, we show that all central extensions which respect the special structure developed here which we term a multimodule Lie-Algebra, are of this form. This result provides a mathemati-cal foundation for non-local conformal field theories, in particular recent proposals in condensed matter in which the current has an anomalous dimension.