Partial Hopf actions, partial invariants and a Morita context
Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions [1]. This allows to extend several results from the theory of partial grou...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154616 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Partial Hopf actions, partial invariants and a Morita context / Marcelo Muniz S. Alves, E. Batista // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 1–19. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862701923789963264 |
|---|---|
| author | Marcelo Muniz S. Alves Batista, E. |
| author_facet | Marcelo Muniz S. Alves Batista, E. |
| citation_txt | Partial Hopf actions, partial invariants and a Morita context / Marcelo Muniz S. Alves, E. Batista // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 1–19. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions [1]. This allows to extend several results from the theory of partial group actions to the Hopf algebraic setting. In this article, we explore some properties of the fixed point subalgebra with relation to a partial action of a Hopf algebra. We also construct, for partial actions of finite dimensional Hopf algebras a Morita context relating the fixed point subalgebra and the partial smash product. This is a generalization of a well known result in the theory of Hopf algebras [9] for the case of partial actions. Finally, we study Hopf-Galois extensions and reobtain some classical results in the partial case.
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| first_indexed | 2025-12-07T16:43:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154616 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:43:53Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Marcelo Muniz S. Alves Batista, E. 2019-06-15T16:53:44Z 2019-06-15T16:53:44Z 2009 Partial Hopf actions, partial invariants and a Morita context / Marcelo Muniz S. Alves, E. Batista // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 3. — С. 1–19. — Бібліогр.: 11 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16W30; 57T05, 16S40, 16S35. https://nasplib.isofts.kiev.ua/handle/123456789/154616 Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to assure the existence of enveloping actions [1]. This allows to extend several results from the theory of partial group actions to the Hopf algebraic setting. In this article, we explore some properties of the fixed point subalgebra with relation to a partial action of a Hopf algebra. We also construct, for partial actions of finite dimensional Hopf algebras a Morita context relating the fixed point subalgebra and the partial smash product. This is a generalization of a well known result in the theory of Hopf algebras [9] for the case of partial actions. Finally, we study Hopf-Galois extensions and reobtain some classical results in the partial case. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Partial Hopf actions, partial invariants and a Morita context Article published earlier |
| spellingShingle | Partial Hopf actions, partial invariants and a Morita context Marcelo Muniz S. Alves Batista, E. |
| title | Partial Hopf actions, partial invariants and a Morita context |
| title_full | Partial Hopf actions, partial invariants and a Morita context |
| title_fullStr | Partial Hopf actions, partial invariants and a Morita context |
| title_full_unstemmed | Partial Hopf actions, partial invariants and a Morita context |
| title_short | Partial Hopf actions, partial invariants and a Morita context |
| title_sort | partial hopf actions, partial invariants and a morita context |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154616 |
| work_keys_str_mv | AT marcelomunizsalves partialhopfactionspartialinvariantsandamoritacontext AT batistae partialhopfactionspartialinvariantsandamoritacontext |