Geodesic
Representations of the deformed oscillator algebra under different choices of generators
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 80-106

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We discuss from unique position different variants of the commutation relations of the algebra of the $q$-deformed boson oscillator related to the different choices of generators. We consider the generalised form of the commutation relations which include as particular cases all of the most popular variants of such relations. By more or less standard way we describe the methods of construction and classification of the representations of the $q$-deformed oscillator algebra under different choices of generators. We also discuss the possibility of introduction the Hopf algebra structure in this algebra. The possibility of construction of the universal ${\mathscr R}$-matrix for considered algebra are also briefly discussed. 
@article{ZNSL_1997_245_a4,
     author = {V. V. Borzov and E. V. Damaskinsky and S. B. Egorov},
     title = {Representations of the deformed oscillator algebra under different choices of generators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--106},
     publisher = {mathdoc},
     volume = {245},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a4/}
}
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V. V. Borzov; E. V. Damaskinsky; S. B. Egorov. Representations of the deformed oscillator algebra under different choices of generators. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 80-106. http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a4/