Hidden classical symmetry in quantum spaces at roots of unity : From q-sphere to fuzzy sphere

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