Partial Hopf actions, partial invariants and a Morita context

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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Bibliographic Details
Date:2018
Main Authors: Alves, Marcelo Muniz S., Batista, Eliezer
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
partial Hopf action
partial group action
partial smash product
Hopf-Galois extensions
16W30; 57T05
16S40
16S35
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-783
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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-04-04T08:43:10Z
collection OJS
language English
topic partial Hopf action
partial group action
partial smash product
Hopf-Galois extensions
16W30; 57T05
16S40
16S35
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
topic_facet partial Hopf action
partial group action
partial smash product
Hopf-Galois extensions
16W30; 57T05
16S40
16S35
format Article
author Alves, Marcelo Muniz S.
Batista, Eliezer
author_facet Alves, Marcelo Muniz S.
Batista, Eliezer
author_sort Alves, Marcelo Muniz S.
title Partial Hopf actions, partial invariants and a Morita context
title_short 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_sort partial hopf actions, partial invariants and a morita context
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.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/783
work_keys_str_mv AT alvesmarcelomunizs partialhopfactionspartialinvariantsandamoritacontext
AT batistaeliezer partialhopfactionspartialinvariantsandamoritacontext
first_indexed 2025-12-02T15:32:37Z
last_indexed 2025-12-02T15:32:37Z
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