0 Spectrum generating algebra and coherent states of the C λ - extended oscillator

C λ-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra , where C λ is the cyclic group of order λ, have recently proved very useful in the context of supersymmetric quantum mechanics and some of its variants. Here we determine the spectrum generating algebra of the C λ-extended oscillator. We then construct its coherent states, study their nonclassical properties, and compare the latter with those of standard λ-photon coherent states, which are obtained as a special case. Finally, we briefly review some other types of coherent states associated with the C λ-extended oscillator.