弱群缠绕结构与弱Hopf群(余)代数(英文)  

WEAK GROUP ENTWINING STRUCTURES AND WEAK HOPF GROUP(CO) ALGEBRAS

作　　者：方小利[1,2] 

机构地区：[1]东南大学数学系,南京210096 [2]绍兴文理学院数学系,绍兴312000

出　　处：《南京大学学报（数学半年刊）》2011年第2期149-167,共19页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by NSF(No.11101288);NSF of Zhejing province(No.Y6110323);Jiangsu planned projects for postdoctoral Research Funds(No.0902081C);Project of Shaoxing University(No.09LG1001)

摘　　要：作为弱Hopf代数与缠绕结构的推广,本文引进弱Hopfπ-代数与弱群缠绕结构,并证明两者之间有着密切的关系：设H={Hα}_（α∈π）是一族余代数同时也是一个余代数.假设A_（αβ）（h_αk_β）△_β（k_β）,则下面几点等价：·H是弱半Hopfπ-代数;·（H,H,ψ′）和（H,H,~2）分别是左-右和左-右弱群缠绕结构;·（H,H,~3）和（H,H,ψ~4）分别是右-左和左-左弱群缠绕结构.最后,作为对偶情形.本文还证明半Hopfπ-余代数与弱群缠绕结构的关系.The so-called weak Hopf π-algebras and weak group entwining structures are defined, which are natural generalizations of the notions weak Hopf algebras and entwining structures introduced by BShm et al. and Brzezifiski et al. respectively. It turns out that the two notions have a nice relationship： Let H = {Hα}α∈π be both a family of coMgebras and a π-Mgebra. Assume thatA_（αβ）（h_αk_β）△_β（k_β）Then the following are equivalent：H is a weak semi-Hopf r-algebra; π （H, H, ψ1） and （H, H, ψ2） are respectively a right-right and a left-right weak group entwining structure; （H, H, ψ3） and （H, H, ψ4） are respectively a right-left and a left-left weak group en- twining structure. Finally, the duM version： the relationship between semi-Hopf r-coalgebras and weak group entwining structures is investigated as well. Keywords weak Hopf lr-Mgebra, weak group entwining structure weak Hopf π- coMgebra

关 键 词：弱Hopf Π-代数 弱群缠绕结构 弱Hopf Π-余代数 

分 类 号：O153[理学—数学]