2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79434Quantum sphere is introduced as a quotient of the so-called Reflection Equation Algebra. This enables us to construct some line bundles on it by means of the Cayley-Hamilton identity whose a quantum version was discovered in \cite{PS}, \cite{GPS}. A new way to introduce some elements of "braided geometry" on the quantum sphere is discussed.LaTex file, 15 pages, minor correction in AcknowledgementQuantum Algebra17B37, 81R50text