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[1] Zhao Qinghu, Zhang Liangyun,. Paired bialgebras and braided bialgebras [J]. Journal of Southeast University (English Edition), 2003, 19 (2): 188-192. [doi:10.3969/j.issn.1003-7985.2003.02.019]
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Paired bialgebras and braided bialgebras()
对偶双代数和辫化双代数
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
19
Issue:
2003 2
Page:
188-192
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2003-06-30

Info

Title:
Paired bialgebras and braided bialgebras
对偶双代数和辫化双代数
Author(s):
Zhao Qinghu1, Zhang Liangyun2
1Department of Mathematics, Nanjing Institute of Meteorology, Nanjing 210044, China
2Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China
赵青虎, 张良云,
南京气象学院数学系, 南京 210044) (南京农业大学数学系, 南京 210095
Keywords:
braided bialgebras;  paired bialgebras;  twisted products;  quadratic bialgebras
辫化双代数;  对偶双代数;  扭曲积;  二次双代数
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2003.02.019
Abstract:
First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler’s 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
通过建立扭曲积和交叉积之间的代数同构, 首先得到了扭曲积的半单性质. 指出了对偶双代数、Yang-Baxter余代数和辫化双代数之间的关系, 并且以四维Sweedler Hopf代数为例来说明. 最后由Yang-Baxter余代数出发, 构造二次双代数使之成为辫化双代数.

References:

[1] Walter R. Twisting products in Hopf algebras and the constructions of the quantum double [J]. Comm in Alg, 1995, 23(7): 2719-2744.
[2] Zhang L Y, Li J Q. The paired bialgebras [J]. Acta Mathematica Sinica, 2000, 43(4): 743-750.
[3] Blattner R J, Montgomery S. Crossed products and galois extensions of Hopf algebras [J]. Pacific Journal of Mathematic, 1989, 137(1): 37-54.
[4] Montgomery S. Hopf algebras and their actions on rings [M]. Providence, Rhode Island: American Mathematical Society, 1993.
[5] Doi Y. Braided bialgebras and quadratic bialgebras [J]. Comm in Alg, 1993, 21(5): 1731-1749.

Memo

Memo:
Biographies: Zhao Qinghu(1968—), male, master; Zhang Liangyun(1964—), male, doctor, associate professor, zlyun8@jlonline.com.
Last Update: 2003-06-20