Yetter-Drinfeld Hopf代数的对偶定理

doi:10.6040/j.issn.1671-9352.0.2014.480

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (12): 98-101.doi: 10.6040/j.issn.1671-9352.0.2014.480

Yetter-Drinfeld Hopf代数的对偶定理

贾玲¹, 陈笑缘²

1. 鲁东大学数学与信息学院, 山东烟台 264025;
2. 浙江商业职业技术学院人文学院, 浙江杭州 310053

收稿日期:2014-11-04 修回日期:2015-03-30 出版日期:2015-12-20 发布日期:2015-12-23
作者简介:贾玲(1974-),女,博士,副教授,研究方向为弱Hopf代数.E-mail:jialing471@126.com
基金资助:
山东省自然科学基金资助项目(ZR2012AL02)

A duality theorem for a Yetter-Drinfeld Hopf algebra

JIA Ling¹, CHEN Xiao-yuan²

1. Department of Mathematics and Information, Ludong University, Yantai 264025, Shandong, China;
2. Faculty of Humanities, Zhejiang Business College, Hangzhou 310053, Zhejiang, China

Received:2014-11-04 Revised:2015-03-30 Online:2015-12-20 Published:2015-12-23

摘要/Abstract

摘要： 证明了Yetter-Drinfeld Hopf代数的对偶定理,得到了对任意交换Yetter-Drinfeld Hopf代数L来说L#L^* 都是半单代数的结论,从而发展了Blattner和Montgomery得到的经典Hopf代数对偶定理。

关键词: 对偶定理, Yetter-Drinfeld Hopf代数, Yetter-Drinfeld模代数

Abstract: A dual theorem for a Yetter-Drinfeld Hopf algebra is given, and it is proved that L#L^* is a semisimple algebra for a cocommutative Yetter-Drinfeld Hopf algebra, which generalizing the classical Blatter-Montgomery dual theorem for Hopf algebras.

Key words: duality theorem, Yetter-Drinfeld Hopf algebra, Yetter-Drinfeld module algebra

中图分类号:

O153.6

贾玲, 陈笑缘. Yetter-Drinfeld Hopf代数的对偶定理[J]. 山东大学学报（理学版）, 2015, 50(12): 98-101.

JIA Ling, CHEN Xiao-yuan. A duality theorem for a Yetter-Drinfeld Hopf algebra[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 98-101.

参考文献

[1] RASFORD D. The structure of Hopf algebras with a projection[J]. J Algebra, 1982, 95:322-347.
[2] LI Libin, ZHANG Pu. Twisted Hopf algebras, Ringel-Hall algebras and Green's category[J]. J Algebra, 2000, 231:713-743.
[3] DOI Y. Hopf modules in Yetter-Drinfeld categories[J]. Comm Algebra, 1998, 26(9):3057-3070.
[4] Van den Bergh M. A duality theorem for Hopf algebras[M]// Methods in Ring Theory. Antwerp, Belgium: Kluwer Academic Publishers, 1984: 517-522.
[5] BLATTER R, Montgomery S. A duality theorem for Hopf module algebras[J]. J Algebra, 1985, 95:153-172.
[6] SCHAUENBURG P. Hopf modules and Yetter-Drinfeld modules[J]. J Algebra, 1994, 169:874-890.
[7] JIA Ling. The structure theorems for Yetter-Drinfeld comodule agebras[J]. Electronic Research Announcements in Mathematical Science, 2013, 20:31-42.

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Yetter-Drinfeld Hopf代数的对偶定理

A duality theorem for a Yetter-Drinfeld Hopf algebra

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