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Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, 36280, Vigo, Spain

    J. N. Alonso Álvarez

  2. Departamento de Álxebra, Universidad de Santiago de Compostela., 15771, Santiago de Compostela, Spain

    J. M. Fernández Vilaboa

  3. Departamento de Matemática Aplicada II, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, 36310, Vigo, Spain

    R. González Rodríguez

Authors
  1. J. N. Alonso Álvarez
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  2. J. M. Fernández Vilaboa
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  3. R. González Rodríguez
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Correspondence to R. González Rodríguez.

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Communicated by Shiping Liu.

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Alonso Álvarez, J.N., Fernández Vilaboa, J.M. & González Rodríguez, R. Fundamental Theorems of Doi–Hopf Modules in a Nonassociative Setting. Bull. Malays. Math. Sci. Soc. 42, 2701–2738 (2019). https://doi.org/10.1007/s40840-018-0624-y

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  • DOI: https://doi.org/10.1007/s40840-018-0624-y

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