## The double covering of the quantum group $$SO_ q (3)$$.(English)Zbl 0833.17019

Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 47-57 (1994).
Summary: A quantum analogue of the double covering of $$\text{SO} (3)$$ by $$\text{SU} (2)$$ is formulated and proved. Here the quantum group $$\text{SO}_q (3)$$ is defined by means of the $$R$$-matrix given by FRT for root systems of type $$B$$. An explicit basis for the deformed function algebra of $$\text{SO}_q (3)$$ is constructed as well as an algorithm to reduce any expression in the generators to a linear combination of basis elements.
For the entire collection see [Zbl 0823.00015].

### MSC:

 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 46L89 Other “noncommutative” mathematics based on $$C^*$$-algebra theory