A duality principle for noncommutative cubes and spheres

Abstract

We discuss a general duality principle, between noncommutative analogues of the standard cube ${\mathbb{Z}}_2^N$, and nonocommutative analogues of the standard sphere $S_{\mathbb{R}}^{N–1}$. This duality is by construction of algebraic geometric nature, and conjecturally connects the corresponding quantum isometry groups, taken in an affine sense.