Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting

In this paper, we introduce the notion of weak nonassociative Doi–Hopf module and give the Fundamental Theorem of Hopf modules in this setting. Also, we prove that there exists a categorical equivalence that admits as particular instances the ones constructed in the literature for Hopf algebras, wea...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2019-09, Vol.42 (5), p.2701-2738
Main Authors: Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Modules
Theorems
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Summary:In this paper, we introduce the notion of weak nonassociative Doi–Hopf module and give the Fundamental Theorem of Hopf modules in this setting. Also, we prove that there exists a categorical equivalence that admits as particular instances the ones constructed in the literature for Hopf algebras, weak Hopf algebras, Hopf quasigroups and weak Hopf quasigroups.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-018-0624-y