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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
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.
Received: August 30, 2016; in final form December 9, 2016; Published online December 11, 2016
Citation:
Theo Johnson-Freyd, “The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions”, SIGMA, 12 (2016), 116, 6 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1198 https://www.mathnet.ru/eng/sigma/v12/p116
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Abstract page: | 127 | Full-text PDF : | 36 | References: | 32 |
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