Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Author: Hasebe, K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146533
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Hopf Maps, Lowest Landau Level, and Fuzzy Spheres / K. Hasebe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 102 назв. — англ.

This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fu...