$C_{ \lambda}$-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where $C_{ \lambda}$ is the cyclic group of order $\lambda$, 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 $C_{ \lambda}$-extended oscillator. We then construct its coherent states, study their nonclassical properties, and compare the latter with those of standard $\lambda$-photon coherent states, which are obtained as a special case. Finally, we briefly review some other types of coherent states associated with the $C_{ \lambda}$-extended oscillator.
Categories: math-ph math.MP