The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|4//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively. We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148553 |
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| Zitieren: | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions / T. Johnson-Freyd // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862641438770069504 |
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| author | Johnson-Freyd, T. |
| author_facet | Johnson-Freyd, T. |
| citation_txt | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions / T. Johnson-Freyd // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|4//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively.
We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|⁴//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively.
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| first_indexed | 2025-12-01T04:42:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148553 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T04:42:35Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Johnson-Freyd, T. 2019-02-18T15:30:26Z 2019-02-18T15:30:26Z 2016 The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions / T. Johnson-Freyd // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15A66; 53D20; 16D90; 81Q60 DOI:10.3842/SIGMA.2016.116 https://nasplib.isofts.kiev.ua/handle/123456789/148553 We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|4//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively. We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|⁴//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively. This paper is a contribution to the Special Issue “Gone Fishing”. The full collection is available at
 http://www.emis.de/journals/SIGMA/gone-fishing2016.html.
 
 I would like to thank the referees for their comments and improvements to this paper. This work
 was completed during the “Gone Fishing 2016” conference at University of Colorado, Boulder,
 which was supported by the NSF grant DMS-1543812. This research was also supported by the
 NSF grant DMS-1304054. The Perimeter Institute for Theoretical Physics is supported by the
 Government of Canada through the Department of Innovation, Science and Economic Development
 Canada and by the Province of Ontario through the Ministry of Research, Innovation and
 Science. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions Article published earlier |
| spellingShingle | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions Johnson-Freyd, T. |
| title | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions |
| title_full | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions |
| title_fullStr | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions |
| title_full_unstemmed | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions |
| title_short | The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions |
| title_sort | quaternions and bott periodicity are quantum hamiltonian reductions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148553 |
| work_keys_str_mv | AT johnsonfreydt thequaternionsandbottperiodicityarequantumhamiltonianreductions AT johnsonfreydt quaternionsandbottperiodicityarequantumhamiltonianreductions |