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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| Datum: | 2018 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543271728185344 |
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| author | Alves, Marcelo Muniz S. Batista, Eliezer |
| author_facet | Alves, Marcelo Muniz S. Batista, Eliezer |
| author_sort | Alves, Marcelo Muniz S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:43:10Z |
| 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. |
| first_indexed | 2025-12-02T15:32:37Z |
| format | Article |
| id | admjournalluguniveduua-article-783 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:37Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7832018-04-04T08:43:10Z Partial Hopf actions, partial invariants and a Morita context Alves, Marcelo Muniz S. Batista, Eliezer partial Hopf action, partial group action, partial smash product, Hopf-Galois extensions 16W30; 57T05, 16S40, 16S35 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783 Algebra and Discrete Mathematics; Vol 8, No 3 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783/313 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | partial Hopf action partial group action partial smash product Hopf-Galois extensions 16W30; 57T05 16S40 16S35 Alves, Marcelo Muniz S. Batista, Eliezer Partial Hopf actions, partial invariants and a Morita context |
| 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 |
| topic | partial Hopf action partial group action partial smash product Hopf-Galois extensions 16W30; 57T05 16S40 16S35 |
| topic_facet | partial Hopf action partial group action partial smash product Hopf-Galois extensions 16W30; 57T05 16S40 16S35 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783 |
| work_keys_str_mv | AT alvesmarcelomunizs partialhopfactionspartialinvariantsandamoritacontext AT batistaeliezer partialhopfactionspartialinvariantsandamoritacontext |