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arXiv · 1603.06603

The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

Theo Johnson-Freyd
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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.

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Theo Johnson-Freyd. 2016-12-11. The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions. https://doi.org/10.3842/sigma.2016.116

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