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 inBulletin of the Malaysian Mathematical Sciences Society Vol. 42; no. 5; pp. 2701 - 2738
Main Authors Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R.
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 15.09.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Modules
Theorems
Hopf quasigroup
18D10
Weak Hopf algebra
20N05
17A30
Fundamental Theorem
16T05
Hopf algebra
Doi–Hopf module
Weak Hopf quasigroup
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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