When ever I hear noncommutative geometers talking about quantum groups, it is usually $qSU(2)$ that they are discussing. As a result there are many good and explicit generator and relation presentations of this Hopf algebra. For an easy example take this other M.O. question. I am curious to see what the simple examples of the other quantum groups series are. More specifically, could anyone give me a generator and relation description of the Hopf algebras $$ qSO(2), ~~~~~~~~~~~~~~~~~~~ qSp(2)? $$ I know that somehow these are derivable from the some quantized enveloping algebra dual quantum groups, but that's a little too difficult for a ''classical'' geometer like me!

If I am not mistaken, $SO(2)\approx U(1)$ has no nontrivial quantum deformation, but $SO(3)$ does; this is explicitly constructed in: Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups, P. Podles (1994) Quantum SO(3) groups, P.M. Soltan (2008) For qSp(2), see Section 3.2 of Noncommutative families of instantons, G. Landi et al. (2008). More general references on quantum classical groups: Quantum deformation of classical groups, T. Hayashi (1992) Quantum symmetric spaces and related qorthogonal polynomials, M. Noumi and T. Sugitani (1995) Orthogonal and symplectic quantum matrix algebras and CayleyHamilton theorem for them, O. Ogievetsky and P. Pyatov (2005) 

