On (p, q; α, β, l)-deformed oscillator and its generalized quantum Heisenberg-Weyl algebra

We present a description of a new kind of the deformed canonical commutation relations, their representations and generated by them generalized quantum Heisenberg-Weyl algebra. This deformed algebra allows us to define operations of the Hopf algebra structure: comultiplication, counit and antipode. We have found out a symmetry of the spectrum of the Hamilton operator of the corresponding deformed harmonic oscillator. (C) 2007 Elsevier B.V. All rights reserved.