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[1]雷思佳,沈远.Hopf双Ore扩张的余乘和对极[J].浙江理工大学学报,2022,47-48(自科六):941-949.
 LEI Sijia,SHEN Yuan.The comultiplications and antipodes of Hopf double Ore extensions[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科六):941-949.
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Hopf双Ore扩张的余乘和对极()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第47-48卷
期数:
2022年自科第六期
页码:
941-949
栏目:
出版日期:
2022-11-10

文章信息/Info

Title:
The comultiplications and antipodes of Hopf double Ore extensions
文章编号:
1673-3851 (2022) 11-0941-09
作者:
雷思佳沈远
浙江理工大学理学院,杭州 310018
Author(s):
LEI Sijia SHEN Yuan
School of Science, Zhengjiang SciTech University, Hangzhou 310018, China
关键词:
Hopf代数双Ore扩张Hopf双Ore扩张余乘对极
分类号:
O153-3
文献标志码:
A
摘要:
为丰富Hopf代数的构造方法以及获得更多Hopf代数实例,引入一般的Hopf(右)双Ore扩张,刻画该扩张的Hopf代数结构。通过余结合性、余单位性和次数的对比,得到Hopf(右)双Ore扩张余乘应具有的3种形式;利用对极是反代数同态,获得Hopf(右)双Ore扩张对极的形式。结果表明:Hopf(右)双Ore扩张中添加的变量在余乘与对极作用下均不包含二元多项式,具有较为简洁的形式。该结果可为后续Hopf代数构造提供帮助。

参考文献/References:

1 Ore O. Theory of non-commutative polynomials J . The Annals of Mathematics, 1933, 34(3): 480-508.

2 Panov A N. Ore extensions of Hopf algebras J . Mathematical Notes, 2003, 74(3): 401-410.

3 Brown K A, O Hagan S, Zhang J J, et al. Connected Hopf algebras and iterated Ore extensions J . Journal of Pure and Applied Algebra, 2015, 219(6): 2405-2433.

4 Huang H D. Hopf Ore extensions J . Algebras and Representation Theory, 2020, 23(4): 1477-1486.

5 Zhuang G B. Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension J . Journal of the London Mathematical Society, 2013, 87(3): 877-898.

6 Wang D G, Zhang J J, Zhuang G. Connected Hopf algebras of Gelfand-Kirillov dimension four J . Transactions of the American Mathematical Society, 2015, 367(8): 5597-5632.

7 Goodearl K R, Zhang J J. Non-affine Hopf algebra domains of Gelfand-Kirillov dimension two J . Glasgow Mathematical Journal, 2017, 59(3): 563-593.

8 Brown K A, Zhang J J. Survey on Hopf algebras of GK-dimension 1 and 2. (2020-03-31) 2022-06-20 . https://doi.org/10 48550/arXiv.2003 - 14251.

9 Zhou G S, Shen Y, Lu D M. The structure of connected (graded) Hopf algebras J . Advances in Mathematics, 2020, 372: 107292.

10 Zhang J J, Zhang J. Double Ore extensions J . Journal of Pure and Applied Algebra, 2008, 212(12):2668-2690.

备注/Memo

备注/Memo:
收稿日期: 2022-06-20
网络出版日期:2022-09-06
基金项目: 国家自然科学基金项目(11701515)
作者简介: 雷思佳(1997-),女,河南信阳人,硕士研究生,主要从事代数学方面的研究
通信作者: 沈远,E-mail:yuanshen@zstu.edu.cn
更新日期/Last Update: 2022-11-07