SUq,h(cross) to 0(2) and SUq,h(cross)(2), the classical and quantum q-deformations of the SU(2) algebra. II. The Hopf algebra, the Yang-Baxter equation and multi-deformed algebraic structures

Abstract

For pt. I see ibid., vol.23, p.4185 (1990). 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.