Poisson Principal Bundles
We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant con...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2021 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211182 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Poisson Principal Bundles. Shahn Majid and Liam Williams. SIGMA 17 (2021), 006, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609687045734400 |
|---|---|
| author | Majid, Shahn Williams, Liam |
| author_facet | Majid, Shahn Williams, Liam |
| citation_txt | Poisson Principal Bundles. Shahn Majid and Liam Williams. SIGMA 17 (2021), 006, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the -Hopf fibration on the standard -sphere. We also construct the Poisson level of the spin connection on a principal bundle.
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| first_indexed | 2026-03-14T06:13:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211182 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T06:13:47Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Majid, Shahn Williams, Liam 2025-12-25T13:24:16Z 2021 Poisson Principal Bundles. Shahn Majid and Liam Williams. SIGMA 17 (2021), 006, 23 pages 1815-0659 2020 Mathematics Subject Classification: 58B32; 53D17; 17B37; 17B62 arXiv:1903.12006 https://nasplib.isofts.kiev.ua/handle/123456789/211182 https://doi.org/10.3842/SIGMA.2021.006 We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the -Hopf fibration on the standard -sphere. We also construct the Poisson level of the spin connection on a principal bundle. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Poisson Principal Bundles Article published earlier |
| spellingShingle | Poisson Principal Bundles Majid, Shahn Williams, Liam |
| title | Poisson Principal Bundles |
| title_full | Poisson Principal Bundles |
| title_fullStr | Poisson Principal Bundles |
| title_full_unstemmed | Poisson Principal Bundles |
| title_short | Poisson Principal Bundles |
| title_sort | poisson principal bundles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211182 |
| work_keys_str_mv | AT majidshahn poissonprincipalbundles AT williamsliam poissonprincipalbundles |