The realizations of quantum groups of A n−1 and C n types in q-deformed oscillator systems at classical and quantum levels

Abstract

In the classical q-deformed oscillators system, the Poisson bracket realizations of the quantum enveloping algebras of An−1 and Cn types are given in the symplectic space (V,Ω) (without deformation). When the oscillators system is canonically quantized, the Lie bracket realizations of the quantum enveloping algebras of An−1 and Cn types are obtained. The Hopf structures of these quantum enveloping algebras are supplied.