Lie Algebroid Connections on Principal Bundles

2025/05/24 by Ghosh, Samit, Arjun Paul, Paul, Arjun
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2505.18821

Abstract

Let X be an irreducible smooth complex projective variety. Let G be a linear algebraic group over ℂ. We define the notion of Lie algebroid valued connection on holomorphic principal G--bundles on X, and study their basic properties under extension and reduction of structure group. Finally we investigate criterions for existence of a Lie algebroid connection on principal G--bundles over smooth complex projective curves.

Citations

• A criterion for Lie algebroid connections on a compact Riemann surface
• Criterion for logarithmic connections with prescribed residues
• Equivariant bundles and connections

Related

• Holomorphic Lie algebroid connections on holomorphic principal bundles on compact Riemann surfaces
• Algebraic Constructions in the Category of Lie Algebroids
• Line bundles on the moduli space of Lie algebroid connections over a curve
• G-Connections on principal bundles over complete G-varieties
• A criterion for Lie algebroid connections on a compact Riemann surface