We present an explicit formulation of the braided symmetries of quantum spheres by introducing a braided quantum Hopf algebra {U}ₐ, and demonstrating that the quantum spheres are {U}ₐ, braided Hopf module algebras. Furthermore, we demonstrate that they are the only quadratic algebras generated by the fundamental representation of {U}ₐ, which are braided {U}ₐ, -modules.
Bistroń et al. (Mon,) studied this question.