共查询到13条相似文献,搜索用时 46 毫秒
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Let k be an algebraically closed field of characteristic zero, and D
n
be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD
n
. We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0). 相似文献
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For a quasi-Hopf algebra H, a left H-comodule algebra and a right H-module coalgebra C we will characterize the category of Doi–Hopf modules C ?(H) in terms of modules. We will also show that for an H-bicomodule algebra and an H-bimodule coalgebra C the category of generalized Yetter–Drinfeld modules (H) C is isomorphic to a certain category of Doi–Hopf modules. Using this isomorphism we will transport the properties from the category of Doi–Hopf modules to the category of generalized Yetter–Drinfeld modules. 相似文献
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For a quasi-Hopf algebra H, an H-bicomodule algebra and an H-bimodule coalgebra C we will show that the category of two-sided two-cosided Hopf modules is equivalent to the category of right–left generalized Yetter–Drinfeld modules . Using alternative versions of this result we will recover the category isomorphism between the categories of left–left and
left–right Yetter–Drinfeld modules over a quasi-Hopf algebra.
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The Yetter-Drinfeld category of the Hopf algebra over a field is a pre braided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD. we prove that the weak biproducts of A and H is a weak Hopf algebra. 相似文献
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高楠 《数学物理学报(B辑英文版)》2008,28(4):870-876
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras. 相似文献
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We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a symmetric monoidal category C.If H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions. 相似文献
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ALONSO LVAREZ Jos Nicanor FERNNDEZ VILABOA Jos Manuel GONZLEZ RODRíIGUEZ Ramón SONEIRA CALVO Carlos 《中国科学 数学(英文版)》2011,(5)
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 cate... 相似文献
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Peter Schauenburg 《Transactions of the American Mathematical Society》2002,354(8):3349-3378
We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by Yetter-Drinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new construction of the Drinfeld double of a quasi-Hopf algebra, as proposed by Majid and constructed by Hausser and Nill.
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Let ?? be a group, and let H be a Hopf ??-coalgebra. We first show that the category M H of right ??-comodules over H is a monoidal category and there is a monoidal endofunctor (F ?? , id, id) of M H for any ?? ?? ??. Then we give the definition of coquasitriangular Hopf ??-coalgebras. Finally, we show that H is a coquasitriangular Hopf ??-coalgebra if and only if M H is a braided monoidal category and (F ?? , id, id) is a braided monoidal endofunctor of M H for any ?? ?? ??. 相似文献