Algebry operatorów i ich zastosowania w fizyce

We begin by recalling the classical Borel-Bott-Weil theorem for complex projective space. Brzezinski and Majid's theory of quantum principal bundles is then recalled, and quantum projective space presented as an example. A connection form is introduced and the induced covariant derivative for the line bundles examined. The notion of a holomorphic structure for a quantum vector bundle, and its associated space of holomorphic sections, is then presented. Finally, the space of holomorphic of the line bundles of quantum projective space is calculated and shown to satisfy a direct q-generalisation of Borel-Bott-Weil.