Operator Realisations of Quantum Heisenberg-Weyl and SU(2) q algebras

The quantum-deformed Heisenberg-Weyl algebra H q and its representations are investigated. The explicit realisations of this q-deformed algebra are founded. A realisation of SU(2) q quantum group with help of only one pair of the bosonic creation and annihilation operators is obtained. Two different cases are discussed: with the use of the q-deformed and the standard Heisenberg-Weyl algebra. Finally a realisation of SU(2) q algebra in the Woronowicz sense is given.