Analytic vectors, anomalies and star representations

It is hinted that anomalies are not really anomalous since (at least in characteristic examples) they can be related to a lack of common analytic vectors for the Hamiltonian and the observables. We reanalyze the notions of analytic vectors and of local representations of Lie algebras in this light, and show how the notion of preferred observables introduced in the deformation (star product) approach to quantization may help give an anomaly-free formulation to physical problems. Finally, some remarks are made concerning the applicability of these considerations to field theory, especially in two dimensions.