發(fā)布時(shí)間：2018-01-14 15:20

  本文關(guān)鍵詞：Hom-纏繞模和Hom-Doi-Hopf模　出處：《河南師范大學(xué)》2015年碩士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： Hom-纏繞模 Hom-Doi-Hopf膜 Hom-smash積 Hom-smash余積 交叉H-Hom-模

【摘要】：近年來(lái),Homm-代數(shù)作為代數(shù)的一類(lèi)形變代數(shù),引起許多學(xué)者的關(guān)注.Homm-(余)代數(shù)是(余)代數(shù)的一個(gè)弱化概念,其(余)結(jié)合性由Homm-(余)代數(shù)的(余)結(jié)合性所替代；即α(a)(bc)=(ab)α(c),(α(a1)(?)a21(?)a22=a11(?)a12(?)α(a2)).本文對(duì)Homm-纏繞模與Hom-smash余)積的關(guān)系、Hom-Doi-Hopf模與交叉H-Hom-模的關(guān)系進(jìn)行研究.主要內(nèi)容如下：(1)先引入Homm-纏繞結(jié)構(gòu)與Hom-Doi-Hopf結(jié)構(gòu),并給出Homm-纏繞模和Hom-Doi-Hopf模的概念.之后,我們研究Homm-纏繞模與Hom-smash(余)積的關(guān)系：若A是Homm-代數(shù),C是有限生成投射Homm-余代數(shù),則在(A,C,ψ)的左-右Homm-纏繞結(jié)構(gòu).HE.(k)與(A,C*,R)的Hom-smash積結(jié)構(gòu)間存在一個(gè)雙射,且左-右Homm-纏繞模范疇AHM(ψ)C與右C*#sA-Hom-余模范疇HMC*#sA同構(gòu).(2)給出Hom-Doi-Hopf模與交叉H-Hom-模的關(guān)系Hom-Doi-Hopf模范疇AHD(H)C和交叉H-Hom-模范疇AHM(Hop (?) H)C同構(gòu)(定理4.1.3).(3)得到Hom-Doi-Hopf模與Hom-smash(余)積的關(guān)系：若(C,αC)是右H-Hom-余模余代數(shù),(D,αD)是右H-Hom-模余代數(shù),則范疇HM(H)CD和HMD×C同構(gòu)(定理4.2.3).若令(B,αB)是右H-Hom-余模代數(shù),(D,αD)是左H-Hom-模余代數(shù),在一定條件下,(?)M ∈B HM(H)D是左B#D*-Hom-模,若D是有限生成投射BHM(H)D等價(jià)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, 偽 ~ (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. 偽 C) is right H-Hom-comodule coalgebra D, 偽 D) is right H-Hom-module coalgebra, then the category HM(H)CD and HMD 脳 C are isomorphic (Theorem 4.2.3). 偽 B) is right H-Hom-comodule algebra D, 偽 D) is left H-Homo -module coalgebra, under certain conditions? M 鈭，

本文編號(hào)：1424159