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
Автор: Hasebe, K.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2010
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/146533
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling 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
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