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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 116, 6 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.116
(Mi sigma1198)
 

This article is cited in 1 scientific paper (total in 1 paper)

The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

Theo Johnson-Freyd

Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
Full-text PDF (337 kB) Citations (1)
References:
Abstract: We show that the Morita equivalences $\mathrm{Cliff}(4) \simeq {\mathbb H}$, $\mathrm{Cliff}(7) \simeq \mathrm{Cliff}(-1)$, and $\mathrm{Cliff}(8) \simeq {\mathbb R}$ arise from quantizing the Hamiltonian reductions ${\mathbb R}^{0|4} // \mathrm{Spin}(3)$, ${\mathbb R}^{0|7} // G_2$, and ${\mathbb R}^{0|8} // \mathrm{Spin}(7)$, respectively.
Keywords: Clifford algebras; quaternions; Bott periodicity; Morita equivalence; quantum Hamiltonian reduction; super symplectic geometry.
Funding agency Grant number
National Science Foundation DMS-1543812
DMS-1304054
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.
Received: August 30, 2016; in final form December 9, 2016; Published online December 11, 2016
Bibliographic databases:
Document Type: Article
Language: English
Citation: Theo Johnson-Freyd, “The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions”, SIGMA, 12 (2016), 116, 6 pp.
Citation in format AMSBIB
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\paper The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
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\vol 12
\papernumber 116
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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