Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
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...
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Дата: | 2010 |
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Формат: | Стаття |
Мова: | English |
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Інститут математики НАН України
2010
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Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146533 |
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Цитувати: | Hopf Maps, Lowest Landau Level, and Fuzzy Spheres / K. Hasebe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 102 назв. — англ. |
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irk-123456789-1465332019-02-10T01:24:57Z Hopf Maps, Lowest Landau Level, and Fuzzy Spheres Hasebe, K. 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. 2010 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
collection |
DSpace DC |
language |
English |
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. |
format |
Article |
author |
Hasebe, K. |
spellingShingle |
Hasebe, K. Hopf Maps, Lowest Landau Level, and Fuzzy Spheres Symmetry, Integrability and Geometry: Methods and Applications |
author_facet |
Hasebe, K. |
author_sort |
Hasebe, K. |
title |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
title_short |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
title_full |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
title_fullStr |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
title_full_unstemmed |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
title_sort |
hopf maps, lowest landau level, and fuzzy spheres |
publisher |
Інститут математики НАН України |
publishDate |
2010 |
url |
http://dspace.nbuv.gov.ua/handle/123456789/146533 |
citation_txt |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres / K. Hasebe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 102 назв. — англ. |
series |
Symmetry, Integrability and Geometry: Methods and Applications |
work_keys_str_mv |
AT hasebek hopfmapslowestlandaulevelandfuzzyspheres |
first_indexed |
2023-05-20T17:25:01Z |
last_indexed |
2023-05-20T17:25:01Z |
_version_ |
1796153239077388288 |