Projective modules over the fuzzy four-sphere

TL;DR

This paper develops a framework for describing projective modules over the fuzzy four-sphere by reducing its algebra to oscillator operators, enabling the explicit construction of instanton connections in a noncommutative geometry setting.

Contribution

It introduces a method to derive projector operators for the fuzzy four-sphere using oscillator operators, providing a global definition of instanton connections.

Findings

Derived projector operators for the fuzzy four-sphere

Established a reduction of the algebra to oscillator operators

Defined k-instanton connections on the noncommutative manifold

Abstract

We describe how to reduce the fuzzy four-sphere algebra to a set of four independent raising and lowering oscillator operators. In terms of them we derive the projector valued operators for the fuzzy four-sphere, which are the global definition of k-instanton connections over this noncommutative base manifold.