Moduli spaces of Hom-Lie algebroid connections

TL;DR

This paper investigates the structure of moduli spaces of Hom-Lie algebroid connections, establishing their Hausdorff Hilbert manifold structure and generalizing known results from classical Lie algebroid theory.

Contribution

It introduces the study of irreducible Hom-Lie algebroid connections and proves the moduli space has a Hausdorff Hilbert manifold structure, extending classical results.

Findings

The H-gauge theoretic moduli space is a Hausdorff Hilbert manifold.

Generalization of results from Lie algebroid connections to Hom-Lie algebroids.

Extension of complex vector bundle connection theory to Hom-Lie algebroids.

Abstract

We have studied irreducible Hom-Lie algebroid connections for Hom-bundle and prove that the H-gauge theoretic moduli space has a Hausdorff Hilbert manifold structure. This work generalizes some known results about simple semi-connections and Lie algebroid connections for complex vector bundles on compact complex manifold.