Hopf代数胚上的Smash积的Maschke型定理和Morita关系（英文）

本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理.     

双边弱smash积的Maschke型定理

本文主要给出半单弱Hopf代数上双边弱Smash积的Maschke型定理.     

偏π-余模的Maschke型定理

本文研究了偏群余模的Mashcke型定理.利用弱Hopf群余代数推广Hopf代数的方法,获得了偏群余模的Mashcke型定理.推广了Hopf代数理论中的Maschke型定理和[8]的相关结论.     

偏π-余模的Maschke型定理（英文）

本文研究了偏群余模的Mashcke型定理.利用弱Hopf群余代数推广Hopf代数的方法,获得了偏群余模的Mashcke型定理.推广了Hopf代数理论中的Maschke型定理和[8]的相关结论.     

弱Hopf代数上的Maschke定理和Morita关系

给出了弱Hopf代数上的Maschke定理, 推广了由Cohen和Fishman给出的著名的Maschke定理, 并且在弱Hopf代数上构造了 Morita关系.     

弱Hopf代数的对偶定理及Smash积的模结构

本文主要包括两方面内容:首先将Hopf代数理论中的对偶定理部分地推广到弱Hopf代数的情况;然后讨论弱Hopf代数上的Smash积的模及模同态,并部分地推广了Maschke-type定理．     

相关Yetter-Drinfel'd Hopf代数上的相关Hopf模结构定理

主要证明了相关Yetter-Drinfel'd Hopf代数上的相关Hopf模结构定理,不仅推广了Yetter-Drinfel'd Hopf代数上的Hopf模结构定理,而且推广了相关Hopf模结构定理.同时,给出相关Yetter-Drinfel'd Hopf代数上的Maschke定理.     

弱模余代数的结构定理

设H为弱Hopf代数,C为弱右H-模余代数,令C=C/C·ker L.利用Smash余积来研究弱模余代数上的结构定理,并给出了C与C×H作为余代数同构的条件.     

乘子Hopf代数的 L-R Smash余积

设 $A$ 是正则乘子Hopf代数, $R$ 是 $A$-\!\!双余模代数, 首先定义了 $A$-\!\!双余模双代数, 并利用它构造了 L-R Smash 积的对偶形式, 即 $R\otimes A$ 上一种非平凡的乘子Hopf代数结构, 称之为 L-R Smash余积. 然后给出了 L-R Smash余积上的积分和$*$-\!\!结构.     

扭Smash双积

设H是双代数 ,A是H 双模代数 ,且为左H 余模余代数 .本文构造一种新的代数—扭Smash双积A×H ,推广了扭Smash积和Smash双积 .我们给出了扭Smash双积A×H作成双代数的充要条件 ,证明了当A ,H都是Hopf代数时 ,A×H 也是Hopf代数 ,利用映射系统刻画了双代数A×H的结构 ,并考虑了它的对偶情况 .     

Products of Linear Maps on Bialgebras,with Applications to Left Hopf Algebras and Hopf Algebroids

The Doi–Koppinen generalized smash product can be applied to linear maps on bialgebras, and we define a new associative product for linear maps on bialgebras. We comment on the applications of these products to left Hopf algebras and Hopf algebroids.     

Maschke-type theorem and Morita context over weak Hopf algebras

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.     

Semidirect products of weak multiplier Hopf algebras: Smash products and smash coproducts

In this paper, we will develop the smash product of weak multiplier Hopf algebras unifying the cases of Hopf algebras, weak Hopf algebras and multiplier Hopf algebras. We will show that the smash product R#A has a regular weak multiplier Hopf algebra structure if R and A are regular weak multiplier Hopf algebras. We shall investigate integrals on R#A. We also consider the result in the ?-situation and new examples. Dually, we consider the smash coproduct of weak multiplier Hopf algebras under an appropriate form and integrals on the smash coproduct and we obtain results in the ?-situation.     

The structure theorem for comodule algebras over Hopf algebroids

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.     

弱Hopf代数作用与冲积

本文研究了弱Hopf代数上的冲积并讨论了它约性质．设H是弱Hopf代数,A是左H-摸代数．我们给出了冲积A#H是弱双代数的一个充分条件以及A#H是A可分扩张的一个判定条件．另外,利用积分理论研究了Hopf模代数的有限性条件．     

External Homogenization for Hopf Algebras: Applications to Maschke's Theorem

We apply to Hopf algebras a construction from graded rings, called the group ring of a graded ring. By using this construction we study the transfer of properties between certain categories of relative Hopf modules. As another application, we obtain a Maschke-type theorem for a Galois extension over a semisimple Hopf algebra.     

Radford's biproduct for quasi-Hopf algebras and bosonization

Let B be a braided Hopf algebra (with bijective antipode) in the category of left Yetter-Drinfeld modules over a quasi-Hopf algebra H. As in the case of Hopf algebras (J. Algebra 92 (1985) 322), the smash product B#H defined in (Comm. Algebra 28(2) (2000) 631) and a kind of smash coproduct afford a quasi-Hopf algebra structure on B⊗H. Using this, we obtain the structure of quasi-Hopf algebras with a projection. Further we will use this biproduct to describe the Majid bosonization (J. Algebra 163 (1994) 165) for quasi-Hopf algebras.     

Hom-弱Hopf代数上的Hom-smash余积

本文研究了在Hom-Hopf代数上引入Hom-弱Hopf代数的问题.利用建立弱左H-Hom-余模双代数的方法,获得了Hom-smash余积的代数结构,并证明了Hom-smash余积是Hom-余代数和Hom-弱Hopf代数,推广了由Molnar定义的smash余积Hopf代数.     

Galois Theory for Multiplier Hopf Algebras with Integrals

In this paper, we introduce a generalized Hopf Galois theory for regular multiplier Hopf algebras with integrals, which might be viewed as a generalization of the Hopf Galois theory of finite-dimensional Hopf algebras. We introduce the notion of a coaction of a multiplier Hopf algebra on an algebra. We show that there is a duality for actions and coactions of multiplier Hopf algebras with integrals. In order to study the Galois (co)action of a multiplier Hopf algebra with an integral, we construct a Morita context connecting the smash product and the coinvariants. A Galois (co)action can be characterized by certain surjectivity of a canonical map in the Morita context. Finally, we apply the Morita theory to obtain the duality theorems for actions and coactions of a co-Frobenius Hopf algebra.