Cλ-EXTENDED OSCILLATOR ALGEBRA AND PARASUPERSYMMETRIC QUANTUM MECHANICS*)

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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 easily exhibited using the representation theory of GDOAs and their carrier spaces 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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