Cleft and Galois extensions associated with a weak Hopf quasigroup

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• 作者：J.N. Alonso Á ; lvarez^a ; ^{jnalonso@uvigo.es" class="auth_mail" title="E-mail the corresponding author} ; J.M. Ferná ; ndez Vilaboa^b ; ^{josemanuel.fernandez@usc.es" class="auth_mail" title="E-mail the corresponding author} ; R. Gonzá ; lez Rodrí ; guez^c ; ^{rgon@dma.uvigo.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：18D10 ; 16T05 ; 17A30 ; 20N05
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：220
• 期：3
• 页码：1002-1034
• 全文大小：560 K

文摘

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.