Some Complex Quantum Manifolds and their Geometry
Abstract
After recalling briefly some basic properties of the quantum group GLq(2), we study the quantum sphere Sq2, quantum projective space CPq(N) and quantum Grassmannians as examples of complex (K\"ahler) quantum manifolds. The differential and integral calculus on these manifolds are discussed. It is shown that many relations of classical projective geometry generalize to the quantum case. For the case of the quantum sphere a comparison is made with A. Connes' method.
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