Atiyah constructions for Lie algebroid connections on fiber bundles
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909656656379904 |
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| author | He, Chen Ni, Dadi Chen, Zhuo |
| author_facet | He, Chen Ni, Dadi Chen, Zhuo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atiyah constructions for Lie algebroid connections on fiber bundles He, Chen Ni, Dadi Chen, Zhuo Differential Geometry Rings and Algebras Primary: 58H05, 17B55, Secondary: 53C05, 55R10 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. |
| title | Atiyah constructions for Lie algebroid connections on fiber bundles |
| topic | Differential Geometry Rings and Algebras Primary: 58H05, 17B55, Secondary: 53C05, 55R10 |
| url | https://arxiv.org/abs/2506.18360 |