# The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

@article{JohnsonFreyd2016TheQA,
title={The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions},
author={T. Johnson-Freyd},
journal={Symmetry Integrability and Geometry-methods and Applications},
year={2016},
volume={12},
pages={116}
}
• T. Johnson-Freyd
• Published 2016
• Mathematics, Physics
• Symmetry Integrability and Geometry-methods and Applications
• 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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