Hom-缠绕模和Hom-Doi-Hopf模

发布时间：2018-01-14 15:20

  本文关键词：Hom-缠绕模和Hom-Doi-Hopf模　出处：《河南师范大学》2015年硕士论文　论文类型：学位论文

  更多相关文章： Hom-缠绕模 Hom-Doi-Hopf膜 Hom-smash积 Hom-smash余积 交叉H-Hom-模

【摘要】：近年来,Homm-代数作为代数的一类形变代数,引起许多学者的关注.Homm-(余)代数是(余)代数的一个弱化概念,其(余)结合性由Homm-(余)代数的(余)结合性所替代；即α(a)(bc)=(ab)α(c),(α(a1)(?)a21(?)a22=a11(?)a12(?)α(a2)).本文对Homm-缠绕模与Hom-smash余)积的关系、Hom-Doi-Hopf模与交叉H-Hom-模的关系进行研究.主要内容如下：(1)先引入Homm-缠绕结构与Hom-Doi-Hopf结构,并给出Homm-缠绕模和Hom-Doi-Hopf模的概念.之后,我们研究Homm-缠绕模与Hom-smash(余)积的关系：若A是Homm-代数,C是有限生成投射Homm-余代数,则在(A,C,ψ)的左-右Homm-缠绕结构.HE.(k)与(A,C*,R)的Hom-smash积结构间存在一个双射,且左-右Homm-缠绕模范畴AHM(ψ)C与右C*#sA-Hom-余模范畴HMC*#sA同构.(2)给出Hom-Doi-Hopf模与交叉H-Hom-模的关系Hom-Doi-Hopf模范畴AHD(H)C和交叉H-Hom-模范畴AHM(Hop (?) H)C同构(定理4.1.3).(3)得到Hom-Doi-Hopf模与Hom-smash(余)积的关系：若(C,αC)是右H-Hom-余模余代数,(D,αD)是右H-Hom-模余代数,则范畴HM(H)CD和HMD×C同构(定理4.2.3).若令(B,αB)是右H-Hom-余模代数,(D,αD)是左H-Hom-模余代数,在一定条件下,(?)M ∈B HM(H)D是左B#D*-Hom-模,若D是有限生成投射BHM(H)D等价于B#D*M.
[Abstract]:In recent years, as a class of deformed algebras, Homm-algebras have attracted the attention of many scholars. Homm-coalgebra is a weakened concept of (coalgebra). The (coassociativity) is replaced by the (coassociativity) of Homm-coalgebra; That is, 伪 ~ (a) a ~ (a) a ~ (a) a ~ (1) a ~ (1) ~ (1) ~ (1) ~ (1) A ~ (1)? A21? A22, A11? A12? ). In this paper, we discuss the relation between Homm-wound mode and Hom-smash coproduct. The relationship between Hom-Doi-Hopf modules and crossed H-Homomodules is studied. The main contents are as follows: 1) first, Homm-winding structure and Hom-Doi-Hopf structure are introduced. The concepts of Homm-wound mode and Hom-Doi-Hopf module are given. We study the relationship between Homm-wound modules and Hom-smash (coproducts): if A is a Homm- algebra C is a finitely generated projective Homm-coalgebra, then it is in Agni C. There is a bijection between the left-right Homm- winding structure. HE. And left to right Homm- wound mode category AHM (蠄 C and right C #sA-Hom-comodule category HMC*#sA isomorphism. 2). Relations between Hom-Doi-Hopf modules and crossed H-Hom-modules Hom-Doi-Hopf module category AHD(H)C and crossed H-Hom-module category AHM (. Hop? The relation between Hom-Doi-Hopf modules and Hom-smash (coproduct) is obtained. 伪 C) is right H-Hom-comodule coalgebra D, 伪 D) is right H-Hom-module coalgebra, then the category HM(H)CD and HMD 脳 C are isomorphic (Theorem 4.2.3). 伪 B) is right H-Hom-comodule algebra D, 伪 D) is left H-Homo -module coalgebra, under certain conditions? M 鈭，

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