Some Complex Quantum Manifolds and their Geometry
High Energy Physics - Theory
2007-05-23 v1
Abstract
After recalling briefly some basic properties of the quantum group , we study the quantum sphere , quantum projective space and quantum Grassmannians as examples of complex (K\"{a}hler) 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.
Cite
@article{arxiv.hep-th/9608188,
title = {Some Complex Quantum Manifolds and their Geometry},
author = {Chong-Sun Chu and Pei-Ming Ho and Bruno Zumino},
journal= {arXiv preprint arXiv:hep-th/9608188},
year = {2007}
}
Comments
Cargese lectures, July 1996, one figure, Full postscript available from http://theor1.lbl.gov/www/theorgroup/papers/39275.ps