Nonsemisimple Quantum Groups as Hopf Algebras of the Dual Functions

Abstract

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 $s{u}_q(2;\mathbf{j})$ are constructed and their isomorphisms with the corresponding quantum orthogonal algebras $s{o}_q(3;\mathbf{j})$ are established. The possible couplings of the Cayley-Klein and Hopf structures are considered.

arXiv comment12 pages, LaTeX