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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
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