  We study the general form of M"obius covariant local commutation relations in
conformal chiral quantum field theories and show that they are intrinsically
determined up to structure constants, which are subject to an infinite system
of constraints. The deformation theory of these commutators is controlled by a
cohomology complex, whose cochain spaces consist of linear maps that are
subject to a complicated symmetry property, a generalization of the
anti-symmetry of the Lie algebra case.
