Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.
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Central Characters of $G_{\mathrm{NC}}$, Darboux Normalization, and the Kinematical Inequivalence of NCQM and QM
Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.