A duality principle for noncommutative cubes and spheres

TL;DR

This paper introduces a duality principle linking noncommutative cubes and spheres through algebraic geometry, potentially connecting their quantum isometry groups.

Contribution

It establishes a new duality framework between noncommutative cubes and spheres, suggesting a deep algebraic geometric connection and conjectural links between their quantum symmetries.

Findings

Proposes a duality principle between noncommutative cubes and spheres.

Suggests a connection between their quantum isometry groups.

Provides a conjectural framework for future research.

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 $S^{N-1}_\mathbb R$. This duality is by construction of algebraic geometric nature, and conjecturally connects the corresponding quantum isometry groups, taken in an affine sense.