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dc.contributor.author |
Hasebe, K. |
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dc.date.accessioned |
2019-02-09T20:29:48Z |
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dc.date.available |
2019-02-09T20:29:48Z |
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dc.date.issued |
2010 |
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dc.identifier.citation |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres / K. Hasebe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 102 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 17B70; 58B34; 81V70 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2010.071 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/146533 |
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dc.description.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. |
uk_UA |
dc.description.sponsorship |
This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The ful`l collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
I would like to thank Yusuke Kimura for collaborations. Many crucial ingredients in this review are based on the works with him. I am also indebted to Takehiro Azuma for email correspondence about mathematics of fuzzy spheres. Since this article is a review-type, many important works not performed by the author are included. Hereby, I express my gratitude to the researchers whose works are reviewed in the paper. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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