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.