Hodge duality operators on left covariant exterior algebras over two and three dimensional quantum spheres

TL;DR

This paper develops Hodge duality operators on differential calculi over quantum spheres and SU(2), utilizing non canonical braidings to extend classical geometric concepts into quantum settings.

Contribution

It introduces a new approach to defining Hodge operators on quantum spheres using non canonical braidings, expanding quantum differential geometry tools.

Findings

Defined symmetric tensors and Hodge operators on 3D quantum SU(2) calculus

Induced Hodge operators on 2D quantum Podles sphere

Extended classical Hodge duality to noncommutative quantum geometries

Abstract

Using non canonical braidings, we first introduce a notion of symmetric tensors and corresponding Hodge operators on a class of left covariant 3d differential calculi over the quantum SU(2) group, then we induce Hodge operators on the left covariant 2d exterior algebras over the standard Podles quantum sphere.