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arXiv · 2506.18360

Atiyah constructions for Lie algebroid connections on fiber bundles

Chen He·Dadi Ni·Zhuo Chen
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Abstract

To address the need for a unified framework that incorporates Lie algebroid connections on both vector and principal bundles, this paper investigates a generalized Atiyah algebroid structure and its short exact sequence. Building on this generalization, we describe Atiyah-type extensions and sequences that represent Atiyah classes through three explicit constructions designed to encode Lie algebroid connections compatible with specified sub-structures. As illustrative examples, we work out an enriched Atiyah algebroid construct, providing a systematic tool to characterize certain key properties of holomorphic connections and invariant connections.

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Chen He, Dadi Ni, Zhuo Chen. 2025-06-23. Atiyah constructions for Lie algebroid connections on fiber bundles. https://arxiv.org/abs/2506.18360

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