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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Published in:	Algebra and Discrete Mathematics
Date:	2009
Main Authors:	Marcelo Muniz S. Alves, Batista, E.
Format:	Article
Language:	English
Published:	Інститут прикладної математики і механіки НАН України 2009
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/154616
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Journal Title:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:	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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	nasplib_isofts_kiev_ua-123456789-154616
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
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Partial Hopf actions, partial invariants and a Morita context
spellingShingle	Partial Hopf actions, partial invariants and a Morita context Marcelo Muniz S. Alves Batista, E.
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
author	Marcelo Muniz S. Alves Batista, E.
author_facet	Marcelo Muniz S. Alves Batista, E.
publishDate	2009
language	English
container_title	Algebra and Discrete Mathematics
publisher	Інститут прикладної математики і механіки НАН України
format	Article
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.
issn	1726-3255
url	https://nasplib.isofts.kiev.ua/handle/123456789/154616
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.
work_keys_str_mv	AT marcelomunizsalves partialhopfactionspartialinvariantsandamoritacontext AT batistae partialhopfactionspartialinvariantsandamoritacontext
first_indexed	2025-12-07T16:43:53Z
last_indexed	2025-12-07T16:43:53Z
_version_	1850868586411720704

Partial Hopf actions, partial invariants and a Morita context

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