Monoidal Hom-Hopf algebra on Hom-twisted product

Let （H, a） be a monoidal Hom-bialgebra and （B,p） be a left （H, a）-Hom-comodule coalgebra. The new monoidal Hom-algebra B#y H is constructed with a Hom-twisted product Ba[H] and a. B × H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B#y / to be a monoidal Hom-bialgebra is given. In addition, let （H, a） be a Hom-σ- Hopf algebra with Hom-〇 --antipode SH, and a sufficient condition for this new monoidal Hom-bialgebra B#y H with the antipode S defined by S（b×h）=（1B×SH（a^-1）b（-1）））（SB（b（0））×1H to be a monoidal Hom-Hopf algebra is derived.

Monoidal Hom-Hopf群-余代数上的Drinfeld量子偶（英文）

本文研究了monoidal Hom-Hopf群-余代数上的Drinfeld量子偶的问题.利用交叉monoidal Hom-Hopf T-余代数的定义及拟三角monoidal Hom-Hopf群-余代数的定义,获得了此Drinfeld量子偶是拟三角monoidal Hom-Hopf群-余代数的结果.

Monoidal Hom-unified积与monoidal Hom-Hopf代数的可裂扩张

从monoidal Hom-Hopf代数的分裂扩张的观点出发,对monoidal Hom-unified积进行等价刻画,即一个monoidal Hom-Hopf代数(E,β)同构于一个monoidal Hom-unified积(A■H,α■γ)当且仅当存在一个可裂单的monoidal Hom-Hopf代数同态i:(A,α)→(E,β).

Doi Hom-Hopf模的Maschke型定理

考虑Doi Hom-Hopf模的半单性或可约性.设(H,A,C)是一个Doi Hom-Hopf-数据,先利用忘却函子将Doi Hom-Hopf模范畴MCA中的对象映为右(A,β)-Hom模范畴MA中对象,再通过对MA中可分单同态进行变形,建立Doi Hom-Hopf-数据积分概念,并利用该积分证明Doi Hom-Hopf模的Maschke型定理.作为应用,定义了Hom-Yetter-Drinfeld模范畴,并证明HomYetter-Drinfeld模范畴是Doi Hom-Hopf模范畴的子范畴,从而得到了Hom-Yetter-Drinfeld模的Maschke型定理.

Monoidal Hom-Hopf代数上的对角交叉积

作为Hopf代数上的对角交叉积的推广,构造了monoidal Hom-Hopf代数上的对角交叉积,并研究了其和Yetter-Drinfeld Hom-模之间的关系,即Yetter-Drinfeld Hom-模范畴同构于对角交叉积的左模范畴。

Center construction and duality of category of Hom-Yetter-Drinfeld modules over monoidal Hom-Hopf algebras

Let （H, α） be a monoidal Hom-Hopf algebra. In this paper, we will study the category of Hom-Yetter-Drinfeld modules. First, we show that the category of left-left Hom-Yetter-Drinfeld modules H^H HYD is isomorphic to the center of the category of left （H, α）-Hom-modules. Also, by the center construction, we get that the categories of left-left, left-right, right-left, and right-right Hom-Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Second, we prove that the category of finitely generated projective left-left Hom-Yetter-Drinfeld modules has left and right duality.

L-R Hom-smash积的Maschke定理（英文）

本文主要给出L-R Hom-smash积成为monoidal Hom-双代数的充要条件以及L-R Hom-smash积的Maschke定理.

偏Hom-模代数的整体化

利用结合子的形变方法,考虑偏Hom-模代数的整体化问题,证明每个偏Hom-模代数均有一个整体化.

偏Hom-模余代数的整体化

通过引入偏Hom-模余代数概念,并考虑了其上的整体化问题,证明了每个偏Hom-模余代数都具有一个整体化.

The cosemisimplicity and cobraided structures of monoidal comonads

In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided category if and only if the monoidal comonad admit a cobraided structure.At last,as an application,the braided structure and the semisimplicity of the Hom-comodule category of a monoidal Hom-bialgebra are discussed.

Hom-Yetter-Drinfeld模范畴的半单性

设k是域,(H,α)是带有双射对极的monoidal Hom-Hopf代数,如果(H,α)是交换的,诺特的,半单和余半单,则Hom-Yetter-Drinfeld模范畴_H HYDH是半单的。也就是说设(H,α)是交换的monoidal Hom-Hopf代数。假设_H HYDH满足某一条件,并且函子(-)^(coH):_H HYD^H→H(M_k)是正合的。如果(M,μ)∈_H HYD^H作为左(H,α)-模是有限生成的,则(M,μ)∈HHYDH保持对象。