# A fuzzy bipolar celestial sphere

## TL;DR

This paper introduces a non-commutative deformation of bipolar spherical harmonics that supports Lorentz symmetry and imposes a maximal angular momentum, advancing the understanding of fuzzy celestial models.

## Contribution

It presents a novel non-commutative algebra for bipolar spherical harmonics compatible with Lorentz symmetry and maximal angular momentum.

## Key findings

- Supports Lorentz algebra action on non-commutative harmonics
- Establishes a maximal angular momentum in the fuzzy model
- Provides explicit Lorentz boost generator actions

## Abstract

We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.