Cλ-extended oscillator algebra and parasupersymmetric quantum mechanics
C. Quesne, N. Vansteenkiste
Abstract
The Cλ-extended oscillator algebra is generated by 1,a,a,N,T, where T is the generator of the cyclic group Cλ of order λ. 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 Zλ grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p= λ- 1.
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