Courant Algebroids. A Short History
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a ''double'' for Lie bialgebroids led to the definition of Courant algebroids. We recount the emergence of these concept...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149218 |
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| Cite this: | Courant Algebroids. A Short History / Y. Kosmann-Schwarzbach // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 55 назв. — англ. |
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Kosmann-Schwarzbach, Y. 2019-02-19T18:58:23Z 2019-02-19T18:58:23Z 2013 Courant Algebroids. A Short History / Y. Kosmann-Schwarzbach // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 55 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 01A65; 53D17; 17B62; 17B66; 22A22; 53C15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.014 https://nasplib.isofts.kiev.ua/handle/123456789/149218 The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a ''double'' for Lie bialgebroids led to the definition of Courant algebroids. We recount the emergence of these concepts. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. I wish to thank Alan Weinstein as well as Dmitry Roytenberg and Pavol Severa for their very ˇ useful correspondence and discussions concerning their work on Courant algebroids. Thanks are also due to Ted Voronov and to the referees for their constructive remarks that were incorporated in the present version. This short history was begun as a memorandum written for Shlomo Sternberg, whom I thank for giving me the incentive to delve into some near-contemporary history. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Courant Algebroids. A Short History Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Courant Algebroids. A Short History |
| spellingShingle |
Courant Algebroids. A Short History Kosmann-Schwarzbach, Y. |
| title_short |
Courant Algebroids. A Short History |
| title_full |
Courant Algebroids. A Short History |
| title_fullStr |
Courant Algebroids. A Short History |
| title_full_unstemmed |
Courant Algebroids. A Short History |
| title_sort |
courant algebroids. a short history |
| author |
Kosmann-Schwarzbach, Y. |
| author_facet |
Kosmann-Schwarzbach, Y. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
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Article |
| description |
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a ''double'' for Lie bialgebroids led to the definition of Courant algebroids. We recount the emergence of these concepts.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149218 |
| citation_txt |
Courant Algebroids. A Short History / Y. Kosmann-Schwarzbach // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 55 назв. — англ. |
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AT kosmannschwarzbachy courantalgebroidsashorthistory |
| first_indexed |
2025-12-07T19:47:17Z |
| last_indexed |
2025-12-07T19:47:17Z |
| _version_ |
1850880124045492224 |