Nonsemisimple Quantum Groups as Hopf Algebras of the Dual Functions

The nonsemisimple quantum Cayley-Klein groups Fun(SU_{q}(2;\bf j}) are realized as Hopf algebra of the noncommutative functions with the dual (or Study) variables. The {\it dual} quantum algebras $su_q(2;{\bf j})$ are constructed and their isomorphisms with the corresponding quantum orthogonal algebras $so_q(3;{\bf j})$ are established. The possible couplings of the Cayley-Klein and Hopf structures are considered.