C_λ-extended oscillator algebra and parasupersymmetric quantum mechanics

Details C_λ-extended oscillator algebra and parasupersymmetric quantum mechanics C_λ-extended oscillator algebra and parasupersymmetric quantum mechanics

1998-08-20

arxiv.org/abs/math/9808092v1

Czech. J. Phys. 48 (1998) 1477-1482

Mathematics

Quantum Algebra

7 pages, LaTeX, no figures, submitted to 7th Int. Coll. ``Quantum Groups and Integrable Systems'', Prague, 18-20 June 1998 (to

Scientific paper

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.

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