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Lie Algebroid Connections on Principal Bundles

Name: Lie Algebroid Connections on Principal Bundles
Keywords: Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, 14J60, 53C07, 32L10, Differential Geometry (math.DG), FOS: Mathematics, Algebraic Geometry (math.AG)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2025Embargo end date: 01 Jan 2025Publisher:arXiv

Authors: Ghosh, Samit; Paul, Arjun;

doi: 10.48550/arxiv.2505.18821

arXiv: http://arxiv.org/abs/2505.18821

Lie Algebroid Connections on Principal Bundles

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Abstract

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. 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.

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Keywords

Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, 14J60, 53C07, 32L10, Differential Geometry (math.DG), FOS: Mathematics, Algebraic Geometry (math.AG)

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