带弱内射的Hopf代数结构

The Structure of Hopf Algebras with a Weak Injection

下载PDF

导出

摘要利用已知Hopf代数构造新的Hopf代数是Hopf代数理论中最基本的问题之一.该文给出了Smash积A#H为Hopf代数,H是A#H的商Hopf代数,且具有弱内射H→A#H的充分必要条件.易证,此种构造推广了Radford和Majid等人所构造的双积和双交叉积等结构. Constructing a new Hopf algebra with known Hopf algebras is one of the most important problems in studying Hopf algebra. In this paper, the authors derive necessary and sufficient conditions for the smash product algebra A#H to be a Hopf algebra with a Hopf quotient algebra H and a weak injection from H to A#H. It is easy to find that this structure includes the Radford’s biproduct and Majid’s bicrossed product as special cases.

作者乐珏张勇

机构地区扬州大学数学科学学院

出处《数学物理学报（A辑）》 CSCD 北大核心 2005年第2期201-212,共12页 Acta Mathematica Scientia

基金国家自然科学基金 (1 0 471 1 2 1 )资助

关键词 HOPF代数交叉积 SMASH积弱内射 Hopf algebra Crossed product Smash product Weak injection。

分类号 O153.3 [理学—基础数学]

引文网络
相关文献

参考文献6

1Radford D E. The structure of Hopf algebras with a projection. J Algebra, 1985, 92: 322-347.
2Schauenburg P. The structure of Hopf algebras with a weak projection. Algebras and Representation Theory, 2000, 3: 187-211.
3陈惠香,刘凌,吴锋,张云.广义Hopf交叉余积[J].数学年刊（A辑）,2003,24(2):245-258. 被引量：3
4Chen H X. Faithful flatness and coflatness of Hopf algebras. Algebra Colloquium, 1999, 6(4): 369-376.
5Schauenburg P. A bialgebra that admits a Hopf-Galois extension is a Hopf algebra. Proceedings of the American Mathematical society, 1997, 125: 83-85.
6Montgomery S. Hopf algebras and their actions on rings. CBMS Series in Math, Am Math Soc, Providence, 1993.

二级参考文献9

1Dascalescu, S., Militarn, G. & Raianu, S., Crossed coproducts and cleft coextensions[J], Comm. Algebra, 24(1996), 1229-1243.
2Doi, Y. & Takeuchi, M., Cleft comodule algebras for a bialgebra [J], Comm. Algebra,14(1986), 801-817.
3Sweedler, M. E., Hopf Algebras [M], Benjamin, New York, 1969.
4Beattie, M., Strongly inner actions, coactions and duality theorems [J], Tsukuba J.Math., 16(1992), 279-293.
5Blattner, R. J., Cohen, M. & Montgomery, S., Crossed products and inner actions of Hopf algebras [J], Trans. Amer. Math. Soc., 298(1986), 671-711.
6Blattner, R. J. & Montgomery, S., Crossed products and Galois extensions of Hopf algebras [J], Pacific J. of Math., 137(1989), 37-54.
7Masuoka, A. & Doi, Y., Generalization of cleft comodule algebras [J], Comm. Algebra,20(1992), 3703-3721.
8Schauenburg, A., Generalization of Hopf crossed product [J], Comm. Algebra, 27(1999),4779-4801.
9Montgomery, S., Hopf algebras and their actions on rings [M], CBMS Series in Math.,Vol.82, Am. Math. Soc., Providence, 1993.

共引文献2

1赵文正,郭静静.(A,H)-相对Hopf模代数和[H,C]-Hopf模余代数[J].河南师范大学学报（自然科学版）,2007,35(2):216-216.
2郭静静,赵文正.相对Hopf模和广义cleft扩张[J].数学杂志,2011,31(3):559-568. 被引量：1

1李涛.双交叉积与斜Pairing[J].淮海工学院学报（自然科学版）,2015,24(1):5-8.
2刘贵龙.Hopf代数的双交叉积[J].数学学报（中文版）,1996,39(1):108-117. 被引量：1
3乐珏,董井成,陈惠香.带弱内射的Hopf代数结构中的特例[J].扬州大学学报（自然科学版）,2003,6(1):4-7.
4张莉娜,倪沈冰.弱Hopf代数的对偶定理及Smash积的模结构[J].Journal of Mathematical Research and Exposition,2006,26(2):369-376.
5李涛.双交叉积上的模范畴[J].赤峰学院学报（自然科学版）,2015,31(6):1-2.
6朱弘鑫.三角Hopf代数表示范畴上的双交叉积[J].复旦学报（自然科学版）,1995,34(2):149-154.
7贾玲,陈笑缘.偏π-余模的Maschke型定理（英文）[J].数学杂志,2017,37(1):21-27.
8陈惠香.斜Pairing,余循环变形与双交叉积[J].数学学报（中文版）,1998,41(5):1065-1068.
9马正义.双交叉积 A#_τH 的投射性[J].丽水学院学报,1999,24(2):3-5.
10陈惠香.双交叉积与余循环变形[J].数学年刊（A辑）,1999,20A(1):39-46.

数学物理学报（A辑）

2005年第2期

浏览历史

内容加载中请稍等...

带弱内射的Hopf代数结构

参考文献6

二级参考文献9

共引文献2

相关作者

相关机构

相关主题

浏览历史