Please wait a minute...
浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (4): 379-388    DOI: 10.3785/j.issn.1008-9497.2016.04.001
数学与计算机科学     
基本弱Hopf代数和弱覆盖箭图
穆尼尔·艾哈迈德1, 李方2
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
Basic weak Hopf algebra and weak covering quiver
AHMED Munir1, LI Fang2
1. Islamabad Model College for Boys, F-10/4, Islamabad, Pakistan;
2. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
 全文: PDF(633 KB)  
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/rkS*.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/IH.
关键词： 弱Hopf代数;  弱覆盖箭图;  分枝数据    
Abstract: 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 S which is isomorphic to the set of all the isomorphism classes of 1-dimensional H-modules such that H/rkS*. 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 H over an algebraically closed field k with strongly graded radical, there exists a weak covering quiver Γ such that kΓ/IH, where the ideal I is generated by the paths of length l≥2.
Key words: weak Hopf algebra    weak covering quiver    ramification data
收稿日期: 2015-09-21 出版日期: 2016-04-28
CLC:  O153  
通讯作者: LI Fang,ORCID:http://orcid.org/0000-0002-4627-1581,E-mail:fangli@zju.edu.cn.     E-mail: fangli@zju.edu.cn
作者简介: AHMEDM(1963-),ORCID:http://orcid.org/0000-0003-4335-6560,male,doctor,assistantprofessor,thefieldofinterestisclassificationandrepresentationofalgebras,E-mail:irmunir@yahoo.com.
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　

引用本文:

穆尼尔·艾哈迈德, 李方. 基本弱Hopf代数和弱覆盖箭图[J]. 浙江大学学报（理学版）, 2016, 43(4): 379-388.

AHMED Munir, LI Fang. Basic weak Hopf algebra and weak covering quiver. Journal of Zhejiang University (Science Edition), 2016, 43(4): 379-388.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.04.001    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I4/379

[1] AUSLANDER M, REITEN I, SMALØ S O. Representation Theory of Artin Algebras, Cambridge Studies in Advance Mathematics 36[M]. New York: Cambridge University Press,1995.
[2] LI F. Weak Hopf algebras and some new solutions of quantum Yang-Baxter equation[J]. Journal of Algebra,1998,208(1):72-100.
[3] LI F. Weak Hopf algebras and regular monoids. ournal of Mathematical Research Exposition,1999,(19):35-331.
[4] CIBILS C, ROSSO M. Hopf quivers.ournal of Algebra,00,54:41-51.
[5] AHMED M, LI F. Self-dual weak Hopf algebras. Acta Mathematica Sinica: English Series,2008,(41):1935-1948.
[6] AHMED M, LI F. Weak Hopf quivers, Clifford monoids and weak Hopf algebras.Arabian ournal for Science and Engineering,2011,36(3):375-39.
[7] GREEN E L, SOLBERG O. Basic Hopf algebra and Quantum groups. Mathematische eitschrift,1998,229(1):45-76.
[8] ASSMAN D, QUINN D. Burnside's theorems of Hopf algebras. roc Amer Math Soc,1995,123(2):37-333.
[9] LI F, CAO H . Semilattice graded weak Hopf algebra and its related quantum G-double. ournal of Mathematical hysics,2005,46(8),083519(1-17).
[10] MONTGOMERY S. Hopf Algebras and Their Actions on Rings CBMS Regional Conference Series in Mathematics[M].New York: American Mathematical Society,1993:38.
[11] SWEEDLER M E. Hopf Algebras[M]. New York: Benjamin INC,1969,26(1):63-65.
[12] CIBILS C, ROSSO M. Algèbres des chemins quantiques. Advances in Mathematics,1997,125(2):171-199.
[13] CIBILS C. The projective class ring of basic and split Hopf algebras. -Theory,1999,17:385-393.
[14] WOODCOC D. Some categorical remarks on the representation of coalgebras. Comm Algebra,1997,25(9):775-794.
[1] 陈笑缘. Cat弱Hopf代数[J]. 浙江大学学报（理学版）, 2017, 44(2): 181-185.
[2] 陈笑缘, 贾玲. 弱广义对角交叉积的表示范畴[J]. 浙江大学学报（理学版）, 2016, 43(6): 672-675.