SUQ,H-]0(2) AND SUQ,H(2), THE CLASSICAL AND QUANTUM Q-DEFORMATIONS OF THE SU(2) ALGEBRA .2. THE HOPF ALGEBRA, THE YANG-BAXTER EQUATION AND MULTI-DEFORMED ALGEBRAIC STRUCTURES

The SUq(2) algebra is realized by means of both the Poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q-deformed oscillators of two different types. The structures of the Hopf algebra and the quantum Yang-Baxter equation are also discussed on a quantum level. A set of j-representations of the quantum algebra SUq(2) is constructed based on the 'type-II' q-oscillators. Multi-deformations of the oscillators of the two types and multi-deformed algebras expressed in Poisson brackets as well as in Lie brackets are proposed.