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Projections of weak braided Hopf algebras 被引量:1
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作者 ALONSO LVAREZ Jos Nicanor FERNNDEZ VILABOA Jos Manuel +1 位作者 GONZLEZ RODRíIGUEZ Ramón SONEIRA CALVO Carlos 《Science China Mathematics》 SCIE 2011年第5期877-906,共30页
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of w... In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal category ofleft-left Yetter-Drinfeld modules over H. 展开更多
关键词 weak Yang-Baxter operator Yetter-Drinfeld module weak (braided) Hopf algebra weak Hopf algebra projection
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A Maschke Type Theorem for Weak Hopf Algebras 被引量:4
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作者 J.N.ALONSOLVAREZ J.M.FERNNDEZVILABOA +1 位作者 R.GONZLEZRODRíGUEZ A.B.RODRíGUEZRAPOSO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第12期2065-2080,共16页
In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. A... In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke's Theorem for (H, B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B. 展开更多
关键词 Monoidal category weak Hopf algebra Hopf modules Maschke Theorem
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Weak crossed biproducts and weak projections
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作者 FERNNDEZ VILABOA Jose Manuel GONZLEZ RODRíGUEZ Ramon RODRíGUEZ RAPOSO Ana Belen 《Science China Mathematics》 SCIE 2012年第7期1321-1352,共32页
In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we comput... In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization. 展开更多
关键词 braided monoidal category preunit crossed product weak Hopf algebra weak projection weakcrossed biproduct
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Strong Connections and Invertible Weak Entwining Structures
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作者 J. N. ALONSO LVAREZ J. M. FERN NDEZ VILABOA GONZ LEZ RODR íGUEZ 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1443-1460,共18页
In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong conne... In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions. 展开更多
关键词 Monoidal category invertible weak entwining structure strong connection weak Galois extension
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