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Lax entwining structures, groupoid algebras and cleft extensions

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Abstract

For an algebra A, a coalgebra C and a lax entwining structure (A, C, ψ), in this paper we introduce the notions of lax C-Galois extension with normal basis and lax C-cleft extension and we prove that these notions are equivalent if the functor A ⊗ — preserve coequalizers.

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Authors and Affiliations

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

    J. N. Alonso Álvarez

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

    J. M. Fernández Vilaboa

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

    R. González Rodríguez

  4. Departamento de Matemáticas, Universidad de Vigo, Campus Universitario de Ourense, E-32004, Ourense, Spain

    C. Soneira Calvo

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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  4. C. Soneira Calvo
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Corresponding author

Correspondence to R. González Rodríguez.

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Alonso Álvarez, J.N., Fernández Vilaboa, J.M., González Rodríguez, R. et al. Lax entwining structures, groupoid algebras and cleft extensions. Bull Braz Math Soc, New Series 45, 133–178 (2014). https://doi.org/10.1007/s00574-014-0044-z

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  • DOI: https://doi.org/10.1007/s00574-014-0044-z

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