The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions - Johnson-Freyd, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|4//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively. We show that the Morita equivalences Cliff(4)≃H, Cliff(7)≃Cliff(−1), and Cliff(8)≃R arise from quantizing the Hamiltonian reductions R⁰|⁴//Spin(3), R⁰|⁷//G₂, and R⁰|⁸//Spin(7), respectively.