Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds
It was recently shown (by the second author and Díaz García, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold q(/ₛ) admits a unique q()-covariant connection with respect to the Heckenberger-Kolb differential calculus Ω¹q(/ₛ). In this paper, we sh...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211718 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds. Alessandro Carotenuto and Réamonn Ó Buachalla. SIGMA 18 (2022), 070, 21 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748302199488512 |
|---|---|
| author | Carotenuto, Alessandro Ó Buachalla, Réamonn |
| author_facet | Carotenuto, Alessandro Ó Buachalla, Réamonn |
| citation_txt | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds. Alessandro Carotenuto and Réamonn Ó Buachalla. SIGMA 18 (2022), 070, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | It was recently shown (by the second author and Díaz García, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold q(/ₛ) admits a unique q()-covariant connection with respect to the Heckenberger-Kolb differential calculus Ω¹q(/ₛ). In this paper, we show that these connections are bimodule connections with an invertible associated bimodule map. This is proved by applying general results of Beggs and Majid, on principal connections for quantum principal bundles, to the quantum principal bundle presentation of the Heckenberger-Kolb calculi recently constructed by the authors and Díaz García. Explicit presentations of the associated bimodule maps are given first in terms of generalised quantum determinants, then in terms of the FRT presentation of the algebra q(), and finally in terms of Takeuchi's categorical equivalence for relative Hopf modules.
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| first_indexed | 2026-04-17T19:46:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211718 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T19:46:53Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Carotenuto, Alessandro Ó Buachalla, Réamonn 2026-01-09T12:43:56Z 2022 Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds. Alessandro Carotenuto and Réamonn Ó Buachalla. SIGMA 18 (2022), 070, 21 pages 1815-0659 2020 Mathematics Subject Classification: 46L87; 81R60; 81R50; 17B37; 16T05 arXiv:2202.09842 https://nasplib.isofts.kiev.ua/handle/123456789/211718 https://doi.org/10.3842/SIGMA.2022.070 It was recently shown (by the second author and Díaz García, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold q(/ₛ) admits a unique q()-covariant connection with respect to the Heckenberger-Kolb differential calculus Ω¹q(/ₛ). In this paper, we show that these connections are bimodule connections with an invertible associated bimodule map. This is proved by applying general results of Beggs and Majid, on principal connections for quantum principal bundles, to the quantum principal bundle presentation of the Heckenberger-Kolb calculi recently constructed by the authors and Díaz García. Explicit presentations of the associated bimodule maps are given first in terms of generalised quantum determinants, then in terms of the FRT presentation of the algebra q(), and finally in terms of Takeuchi's categorical equivalence for relative Hopf modules. AC was supported by the GAČR project 20-17488Y and RVO: 67985840. AC and RÓB are supported by the Charles University PRIMUS grant Spectral Noncommutative Geometry of Quantum Flag Manifolds PRIMUS/21/SCI/026. We would like to thank Henrik Winther for the useful discussions. Moreover, we would like to thank the referees for their careful reading of the paper and their helpful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds Article published earlier |
| spellingShingle | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds Carotenuto, Alessandro Ó Buachalla, Réamonn |
| title | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds |
| title_full | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds |
| title_fullStr | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds |
| title_full_unstemmed | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds |
| title_short | Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds |
| title_sort | bimodule connections for relative line modules over the irreducible quantum flag manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211718 |
| work_keys_str_mv | AT carotenutoalessandro bimoduleconnectionsforrelativelinemodulesovertheirreduciblequantumflagmanifolds AT obuachallareamonn bimoduleconnectionsforrelativelinemodulesovertheirreduciblequantumflagmanifolds |