Representations of the deformed oscillator algebra for different choices of generators

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For the q-deformed boson oscillator algebra, different commutation relations corresponding, to different choices of generators are considered in the general context. By the standard technique, the problems of construction and classification of the 1-deformed boson oscillator algebra representations in different bases are solved. The possibility of introducing the Hopf algebra structure in the q-deformed oscillator algebra is considered. The possibility of constructing the universal R-matrix for the algebra under consideration is briefly discussed. Bibliography: 20 titles.