The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

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.

References in corpus (2)

• A supergeometric approach to Poisson reduction
• On homotopy Poisson actions and reduction of symplectic Q-manifolds