Produção Nacional
Revisado por pares
Dilations of partial representations of Hopf algebras
2019; Wiley; Volume: 100; Issue: 1 Linguagem: Inglês
10.1112/jlms.12213
ISSN1469-7750
AutoresMarcelo Muniz S. Alves, Eliezer Batista, Joost Vercruysse,
Tópico(s)Advanced Operator Algebra Research
ResumoJournal of the London Mathematical SocietyVolume 100, Issue 1 p. 273-300 Research Article Dilations of partial representations of Hopf algebras Marcelo Muniz S. Alves, Marcelo Muniz S. Alves marcelomsa@ufpr.br Departamento de Matemática - UFPR, Centro Politécnico, C.P. 19096, 81531-980 Curitiba - PR, BrazilSearch for more papers by this authorEliezer Batista, Eliezer Batista ebatista@mtm.ufsc.br Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Universitário Trindade, 88.040-900 Florianópolis-SC, BrazilSearch for more papers by this authorJoost Vercruysse, Joost Vercruysse jvercruy@ulb.ac.be Université Libre de Bruxelles, Campus "Plaine", Boulevard du triomphe, B1050 Brussels, BelgiumSearch for more papers by this author Marcelo Muniz S. Alves, Marcelo Muniz S. Alves marcelomsa@ufpr.br Departamento de Matemática - UFPR, Centro Politécnico, C.P. 19096, 81531-980 Curitiba - PR, BrazilSearch for more papers by this authorEliezer Batista, Eliezer Batista ebatista@mtm.ufsc.br Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Universitário Trindade, 88.040-900 Florianópolis-SC, BrazilSearch for more papers by this authorJoost Vercruysse, Joost Vercruysse jvercruy@ulb.ac.be Université Libre de Bruxelles, Campus "Plaine", Boulevard du triomphe, B1050 Brussels, BelgiumSearch for more papers by this author First published: 28 February 2019 https://doi.org/10.1112/jlms.12213Citations: 5 The first author is partially supported by CNPq, grant number 306583/2016-0. The third author would like to thank the FWB (Fédération Wallonie-Bruxelles) for financial support via the ARC-project 'Hopf algebras and the symmetries of non-commutative spaces' as well as the FNRS for the MIS-project 'Antipode'. All authors thank the anonymous referee for his/her useful comments that improved the presentation of this paper. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract We introduce the notion of a dilation for a partial representation (that is, a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (that is, a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial H-modules, a category of (global) H-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon H, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory. Citing Literature Volume100, Issue1August 2019Pages 273-300 RelatedInformation
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