南京大学学报（数学半年刊）
南京大學學報（數學半年刊）
남경대학학보（수학반년간）
JOURNAL OF NANJING UNIVERSITY MATHEMATICAL BIQUARTERLY
2011年
2期
149-167
,共19页
弱Hopfπ-代数%弱群缠绕结构%弱Hopfπ-余代数
弱Hopfπ-代數%弱群纏繞結構%弱Hopfπ-餘代數
약Hopfπ-대수%약군전요결구%약Hopfπ-여대수
weak Hopf π-algebra%weak%group%entwining%structure%weak%Hopf%πcoalgebra
作为弱Hopf代数与缠绕结构的推广,本文引进弱Hopf π-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Aαβ(hαkβ)△β(kβ),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,ψ4)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.
作為弱Hopf代數與纏繞結構的推廣,本文引進弱Hopf π-代數與弱群纏繞結構,併證明兩者之間有著密切的關繫:設H={Hα}α∈π是一族餘代數同時也是一箇餘代數.假設Aαβ(hαkβ)△β(kβ),則下麵幾點等價:·H是弱半Hopfπ-代數；·(H,H,ψ')和(H,H,2)分彆是左-右和左-右弱群纏繞結構；·(H,H,3)和(H,H,ψ4)分彆是右-左和左-左弱群纏繞結構.最後,作為對偶情形,本文還證明半Hopfπ-餘代數與弱群纏繞結構的關繫.
작위약Hopf대수여전요결구적추엄,본문인진약Hopf π-대수여약군전요결구,병증명량자지간유착밀절적관계:설H={Hα}α∈π시일족여대수동시야시일개여대수.가설Aαβ(hαkβ)△β(kβ),칙하면궤점등개:·H시약반Hopfπ-대수；·(H,H,ψ')화(H,H,2)분별시좌-우화좌-우약군전요결구；·(H,H,3)화(H,H,ψ4)분별시우-좌화좌-좌약군전요결구.최후,작위대우정형,본문환증명반Hopfπ-여대수여약군전요결구적관계.
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 B(o)hm et al.and Brzezi(n)ski et al.respectively.It turns out that the two notions have a nice relationship:Let H ={Hα}α∈π be both a family of coalgebras and a π-algebra.Assume that △αβ(hαkβ) =△α(hα)△β(kβ).Then the following are equivalent:· H is a weak semi-Hopf π-algebra;· (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 entwining structure.Finally,the dual version:the relationship between semi-Hopf π-coalgebras and weak group entwining structures is investigated as well.
