Moduli of real (res. quaternionic) L-connections

TL;DR

This paper investigates the structure of moduli spaces of real and quaternionic Lie algebroid connections, establishing their manifold properties and generalizing known results from complex algebraic geometry.

Contribution

It introduces a framework for understanding the moduli space of irreducible real and quaternionic Lie algebroid connections, proving their Hausdorff Hilbert manifold structure.

Findings

Moduli space of connections is a Hausdorff Hilbert manifold.

Generalizes results from complex vector bundle semi-connections.

Extends understanding of gauge theory in real and quaternionic settings.

Abstract

We have studied irreducible real (respectively, quaternionic) Lie algebroid connections and prove that the Gauge theoretic moduli space has Hausdorff Hilbert manifold structure. This work generalises some known results about simple semi-connections for complex vector bundle on compact complex manifold in real algebraic geometry.