Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
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| Creator |
Hasebe, K.
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| Description |
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.
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| Date |
2019-02-09T20:29:48Z
2019-02-09T20:29:48Z 2010 |
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| Type |
Article
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| Identifier |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres / K. Hasebe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 102 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 17B70; 58B34; 81V70 DOI:10.3842/SIGMA.2010.071 http://dspace.nbuv.gov.ua/handle/123456789/146533 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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