Notes on generalised spin structures
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915600261971968 |
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| author | Beckett, Andrew D. K. |
| author_facet | Beckett, Andrew D. K. |
| contents | We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop a covariant Cartan calculus. We introduce an extension of the Lie algebra of Killing vectors, the symmetry algebra, and show that it has a representation on sections of associated bundles. We discuss homogeneous generalised spin structures and provide a characterisation of them in terms of lifts of the isotropy representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on generalised spin structures Beckett, Andrew D. K. Differential Geometry High Energy Physics - Theory 53C27 (Primary) 17B66 (Secondary) We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop a covariant Cartan calculus. We introduce an extension of the Lie algebra of Killing vectors, the symmetry algebra, and show that it has a representation on sections of associated bundles. We discuss homogeneous generalised spin structures and provide a characterisation of them in terms of lifts of the isotropy representation. |
| title | Notes on generalised spin structures |
| topic | Differential Geometry High Energy Physics - Theory 53C27 (Primary) 17B66 (Secondary) |
| url | https://arxiv.org/abs/2511.03627 |