Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting

  • J. N. Alonso Álvarez
  • J. M. Fernández Vilaboa
  • R. González Rodríguez


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.


Hopf algebra Weak Hopf algebra Hopf quasigroup Weak Hopf quasigroup Doi–Hopf module Fundamental Theorem 

Mathematics Subject Classification

18D10 16T05 17A30 20N05 



The authors were supported by Ministerio de Economía y Competitividad (Spain), grant MTM2016-79661-P. AEI/FEDER, UE, support included (Homología, homotopía e invariantes categóricos en grupos y álgebras no asociativas).


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  • J. N. Alonso Álvarez
    • 1
  • J. M. Fernández Vilaboa
    • 2
  • R. González Rodríguez
    • 3
  1. 1.Departamento de MatemáticasUniversidad de VigoVigoSpain
  2. 2.Departamento de ÁlxebraUniversidad de Santiago de Compostela.Santiago de CompostelaSpain
  3. 3.Departamento de Matemática Aplicada IIUniversidad de VigoVigoSpain

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