Fundamental theorem of \((A,\mathcal G,H)\)-comodules
Let \(k\) be a field, \(H\) a Hopf algebra with a bijective antipode, \(\mathcal G\) an \(H\)-comodule Lie algebra and \(A\) a commutative \(({\mathcal G},H)\)-comodule algebra. We assume that there is an \(H\)-colinear algebra map from \(H\) to \(A^{\mathcal G}\). We generalize the Fundamental Theo...
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| Datum: | 2025 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2025
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543146532405248 |
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| author | Guédénon, Thomas |
| author_facet | Guédénon, Thomas |
| author_sort | Guédénon, Thomas |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2025-10-27T20:24:52Z |
| description | Let \(k\) be a field, \(H\) a Hopf algebra with a bijective antipode, \(\mathcal G\) an \(H\)-comodule Lie algebra and \(A\) a commutative \(({\mathcal G},H)\)-comodule algebra. We assume that there is an \(H\)-colinear algebra map from \(H\) to \(A^{\mathcal G}\). We generalize the Fundamental Theorem of \((A,H)\)-Hopf modules to \((A,{\mathcal G},H)\)-comodules, and we deduce relative projectivity in the category of \((A,{\mathcal G},H)\)-comodules. In many applications, \(A\) could be a commutative \(G\)-graded \(\mathcal G\)-module algebra, where \(G\) is an abelian group and \(\mathcal G\) is a \(G\)-graded Lie algebra; or a rational \(({\mathcal G},G)\)-module algebra, where \(G\) is an affine algebraic group and \(\mathcal G\) is a rational \(G\)-module Lie algebra. |
| first_indexed | 2025-12-02T15:56:12Z |
| format | Article |
| id | admjournalluguniveduua-article-2345 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:56:12Z |
| publishDate | 2025 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-23452025-10-27T20:24:52Z Fundamental theorem of \((A,\mathcal G,H)\)-comodules Guédénon, Thomas Lie algebra, module over a Lie algebra, Hopf algebra, Hopf module, \(H\)-comodule Lie algebra, \(({\mathcal G},H)\)-comodule algebra, \((A,{\mathcal G},H)\)-comodule Primary: 16T05. Secondary: 17B60 Let \(k\) be a field, \(H\) a Hopf algebra with a bijective antipode, \(\mathcal G\) an \(H\)-comodule Lie algebra and \(A\) a commutative \(({\mathcal G},H)\)-comodule algebra. We assume that there is an \(H\)-colinear algebra map from \(H\) to \(A^{\mathcal G}\). We generalize the Fundamental Theorem of \((A,H)\)-Hopf modules to \((A,{\mathcal G},H)\)-comodules, and we deduce relative projectivity in the category of \((A,{\mathcal G},H)\)-comodules. In many applications, \(A\) could be a commutative \(G\)-graded \(\mathcal G\)-module algebra, where \(G\) is an abelian group and \(\mathcal G\) is a \(G\)-graded Lie algebra; or a rational \(({\mathcal G},G)\)-module algebra, where \(G\) is an affine algebraic group and \(\mathcal G\) is a rational \(G\)-module Lie algebra. Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345 10.12958/adm2345 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1260 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1269 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1270 Copyright (c) 2025 Algebra and Discrete Mathematics |
| spellingShingle | Lie algebra module over a Lie algebra Hopf algebra Hopf module \(H\)-comodule Lie algebra \(({\mathcal G},H)\)-comodule algebra \((A,{\mathcal G},H)\)-comodule Primary: 16T05. Secondary: 17B60 Guédénon, Thomas Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title | Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title_full | Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title_fullStr | Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title_full_unstemmed | Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title_short | Fundamental theorem of \((A,\mathcal G,H)\)-comodules |
| title_sort | fundamental theorem of \((a,\mathcal g,h)\)-comodules |
| topic | Lie algebra module over a Lie algebra Hopf algebra Hopf module \(H\)-comodule Lie algebra \(({\mathcal G},H)\)-comodule algebra \((A,{\mathcal G},H)\)-comodule Primary: 16T05. Secondary: 17B60 |
| topic_facet | Lie algebra module over a Lie algebra Hopf algebra Hopf module \(H\)-comodule Lie algebra \(({\mathcal G},H)\)-comodule algebra \((A,{\mathcal G},H)\)-comodule Primary: 16T05. Secondary: 17B60 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345 |
| work_keys_str_mv | AT guedenonthomas fundamentaltheoremofamathcalghcomodules |