Geometry of the Quantum Complex Projective Space $CP_q(N)$

Details Geometry of the Quantum Complex Projective Space $CP_q(N)$ Geometry of the Quantum Complex Projective Space $CP_q(N)$

1995-10-21

arxiv.org/abs/q-alg/9510021v1

Z.Phys. C72 (1996) 163-170

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

10.1007/s002880050233

The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum K\"{a}hler manifold. The braiding of several copies of $CP_q(N)$ is introduced and the anharmonic ratios of four collinear points are shown to be invariant under quantum projective transformations. They provide the building blocks of all projective invariants. The Poisson limit is also described.

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