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This article is cited in 36 scientific papers (total in 36 papers)
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
Kazuki Hasebe Kagawa National College of Technology, Mitoyo, Kagawa 769-1192, Japan
Abstract:
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 fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of “compounds” of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.
Keywords:
division algebra; Clifford algebra; Grassmann algebra; Hopf map; non-Abelian monopole; Landau model; fuzzy geometry.
Received: May 5, 2010; in final form August 19, 2010; Published online September 7, 2010
Citation:
Kazuki Hasebe, “Hopf Maps, Lowest Landau Level, and Fuzzy Spheres”, SIGMA, 6 (2010), 071, 42 pp.
Linking options:
https://www.mathnet.ru/eng/sigma529 https://www.mathnet.ru/eng/sigma/v6/p71
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