An obstruction to quantization of the sphere

Abstract

In the standard example of strict deformation quantization of the symplectic sphere S2, the set of allowed values of the quantization parameter Latin small letter h with stroke is not connected; indeed, it is almost discrete. Li recently constructed a class of examples (including S 2) in which Latin small letter h with stroke 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 S2 is never connected.