An obstruction to quantization of the sphere

In the standard example of strict deformation quantization of the symplectic sphere S-2, the set of allowed values of the quantization parameter (h) over bar is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S-2) in which (h) over bar can take any value in an interval, but these examples are badly behaved. Here, I identify a natural additional axiom for strict deformation quantization and prove that it implies that the parameter set for quantizing S-2 is never connected.