The quantum spheres and their embedding into quantum Minkowski space-time (Q1854125)

The author recasts the quantum spheres in the noncommutative special relativity. It is first shown that the Podles spheres [\textit{P. Podles}, Lett. Math. Phys. 14, 193-202 (1987; Zbl 0634.46054)] can be regarded as quantum manifolds embedded into the quantum Minkowski space-time. This embedding is shown to preserve the commutation rules of the quantum Minkowski space-time. Then, the author shows that the state transformations under the coaction of the \(SO_q(3)\) groups exhibits the periodicity of the quantum sphere states through a decomposition of the Hilbert space in terms of orthogonal subspaces.