Cleft and Galois extensions associated with a weak Hopf quasigroup

• J.N. Alonso Álvarez ^[1] ; J.M. Fernández Vilaboa ^[2] ; R. González Rodríguez ^[1]
  1. [1] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
  2. [2] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 3 (March 2016), 2016, págs. 1002-1034
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.08.005
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• Resumen

  • In this paper we introduce the notions of cleft and Galois (with normal basis) extension associated with a weak Hopf quasigroup. We show that, under suitable conditions, both notions are equivalent. As a particular instance we recover the classical results for (weak) Hopf algebras. Moreover, taking into account that weak Hopf quasigroups generalize the notion of Hopf quasigroup, we obtain the definitions of cleft and Galois (with normal basis) extension associated with a Hopf quasigroup and we get the equivalence between these extensions in this setting.