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The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Theo Johnson-Freyd},
     title = {The {Quaternions} and {Bott} {Periodicity} {Are} {Quantum} {Hamiltonian} {Reductions}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a115/}
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Theo Johnson-Freyd. The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a115/

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