共查询到20条相似文献,搜索用时 0 毫秒
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G. C. Wraith 《Annali di Matematica Pura ed Applicata》1967,76(1):149-163
Summary In any category with products and a terminal object one may define the notions of group, module over a group etc. if f: R′→R
is a homomorphism of groups, and M an R-module, then one has an induced R′-module f*(M). If one is working in the category
of sets, one may define a functor left adjoint to f* by N→R⊗R′ N, where N is an R′-module. In this paper we show that f* has a left adjoint when one is working in the category of graded
connected coalgebras over a field. 相似文献
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Zhi-xiang Wu 《高校应用数学学报(英文版)》2018,33(1):107-126
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized. 相似文献
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Martín Mombelli 《Mathematische Zeitschrift》2010,266(2):319-344
We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras.
As an application we classify exact module categories over the tensor category of representations of the small quantum groups
uq(\mathfraksl2){u_q(\mathfrak{sl}_2)}. 相似文献
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We study the realizations of certain braided vector spaces of rack type as Yetter–Drinfeld modules over a cosemisimple Hopf algebra H. We apply the strategy developed in [1] to compute their liftings and use these results to obtain the classification of finite-dimensional copointed Hopf algebras over . 相似文献
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We prove a result on the transfer of essentiality of extensions of modules over subnormalizing extensions of rings, then apply it to look at the semiprimeness of Hopf-Galois extensions, in particular that of crossed products.
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LIU Gongxiang & YE Yu Institute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(3):320-329
In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras. 相似文献
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It is proved in the paper that a Noetherian residually finite-dimensional Hopf algebra H is a flat module over any right Noetherian right coideal subalgebra A. In the case when A is a Hopf subalgebra we get faithful flatness. These results are obtained by verifying the existence of classical quotient rings of A and H. It is also proved that the antipode of either right or left Noetherian residually finite-dimensional Hopf algebra is bijective. As a consequence, such a Hopf algebra is right and left Noetherian simultaneously.
相似文献9.
We study indecomposable codes over a family of Hopf algebras introduced by Radford. We use properties of Hopf algebras to show that tensors of ideal codes are ideal codes, extending the corresponding result that was previously given in the case of Taft Hopf algebras and showing the differences with that case. 相似文献
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J. CuadraJ.M. García-Rubira J.A. López-Ramos 《Journal of Computational and Applied Mathematics》2011,235(7):1833-1839
We determine all indecomposable codes over a class of Hopf algebras named Taft Algebras. We calculate dual codes and tensor products of these indecomposable codes and give applications of them. 相似文献
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Fernando Fantino Gastón Andrés García Mitja Mastnak 《Journal of Pure and Applied Algebra》2019,223(8):3611-3634
We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions over a dihedral group , with . We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups. 相似文献
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We obtain the structure theorem for $(H, \mathcal{H})$ -Hopf bimodules over Hopf algebroids, where H is the total algebra of the Hopf algebroid $\mathcal{H}$ . Based on this theorem, we investigate the structure theorem for comodule algebras over Hopf algebroids. 相似文献
17.
Maschke-type theorem and Morita context over weak Hopf algebras 总被引:8,自引:0,他引:8
ZHANG Liangyun College of Science Nanjing Agricultural University Nanjing China Department of Mathematics Nanjing University Nanjing China 《中国科学A辑(英文版)》2006,49(5):587-598
This paper gives a Maschke-type theorem over semisimple weak Hopf algebras, extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras. 相似文献
18.
George E. Andrews Li Guo William Keigher Ken Ono 《Transactions of the American Mathematical Society》2003,355(11):4639-4656
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
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