  We study relations between different kinds of non-commutative spheres which
have appeared in the context of ADS/CFT correspondences recently, emphasizing
the connections between spaces that have manifest quantum group symmetry and
spaces that have manifest classical symmetry. In particular we consider the
quotient $SU_q(2)/U(1)$ at roots of unity, and find its relations with the
fuzzy sphere with manifest classical SU(2) symmetry. Deformation maps between
classical and quantum symmetry, the $U_q(SU(2))$ module structure of quantum
spheres and the structure of indecomposable representations of $U_q(SU(2))$ at
roots of unity conspire in an interesting way to allow the relation between
manifestly $U_q(SU(2)$ symmetric spheres and manifestly U(SU(2)) symmetric
spheres. The relation suggests that a subset of field theory actions on the
q-sphere are equivalent to actions on the fuzzy sphere. The results here are
compatible with the proposal that quantum spheres at roots of unity appear as
effective geometries which account for finite N effects in the ADS/CFT
correspondence.
