C_(λ)-extended oscillator algebra and parasupersymmetric quantum mechanics

The C_{\lambda}-extended oscillator algebra is generated by {1,a,a^{\dagger},N,T}, where T is the generator of the cyclic group C_{\lambda} of order \lambda. It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be exhibited using the representation theory of GDOAs and their carrier space show a Z_{\lambda} grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p= \lambda - 1.