Algebry operatorów i ich zastosowania w fizyce

Consider closed refinement of a canonical covering ofa projective space. Projective space can be then viewed as amulti-pushout of the family of covering sets. We dualize the construction and substitute polydiscs with appropriate tensor powers of a Toeplitz algebra. This gives rise to the family of quantum projective spaces.We focus on dimension two in which we construct appropriatequantum spheres (principal bundles) and then tautological line bundles as a associated bundles. We then prove non-triviality of such defined bundles.