基本弱Hopf代数和弱覆盖箭图（英文）  

Basic weak Hopf algebra and weak covering quiver

作　　者：穆尼尔·艾哈迈德 李方[2] 

机构地区：[1]伊斯兰堡大学模范男子学院,巴基斯坦伊斯兰堡 [2]浙江大学数学科学学院,浙江杭州310027

出　　处：《浙江大学学报（理学版）》2016年第4期379-388,410,共11页Journal of Zhejiang University（Science Edition）

基　　金：Supported by the National Natural Science Foundation of China(11271318,11571173);the Zhejiang Provincial Natural Science Foundation of China(LZ13A010001)

摘　　要：研究了代数闭域K上具有强分次Jacobson根r的有限维基本可裂弱Hopf代数,并刻画了有限维基本可裂半格分次弱Hopf代数H,即存在有限Clifford半群S,使得H/r■kS*.还引入了弱覆盖箭图的概念,其路代数具有半格分次弱Hopf代数的结构,其箭图作为弱覆盖箭图被刻画.进一步地,证明了对上述H存在弱覆盖箭图Г和由长度大于2的路生成的理想I,使得kГ/I■H.We introduce a finite-dimensional basic and split weak Hopf algebra H over an algebraically closed field k with strongly graded Jacobson radical r.We obtain some structures of a finite-dimensional basic and split semilattice graded weak Hopf algebra,and observe that there exists a finite Clifford monoid Swhich is isomorphic to the set of all the isomorphism classes of 1-dimensional H-modules such that H/r■kS＊.We also introduce the notion of weak covering quiver whose path algebra admits a structure of semilattice graded weak Hopf algebra,and classify the path algebra corresponding to the weak covering quiver.Furthermore,we prove that,for a finite-dimensional basic semilattice graded weak Hopf algebra Hover an algebraically closed field k with strongly graded radical,there exists a weak covering quiverΓsuch that kΓ/I■H,where the ideal Iis generated by the paths of length l≥2.

关 键 词：弱HOPF代数 弱覆盖箭图 分枝数据 

分 类 号：O153[理学—数学]