Deformed Virasoro algebra from Feigin-Fuks construction

The Virasoro algebra is the symmetry algebra of two-dimensional conformal theories. It is the universal central extension of the Witt algebra, the Lie algebra of vector fields on the circle. Several constructions allow to deduce the Virasoro algebra from the Witt algebra, most notably the Feigin-Fuks construction. I'll discuss a more general framework of this construction and apply it to a q-deformed Witt algebra, giving a new deformation of the Virasoro algebra.