|Table of Contents|

[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()
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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
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
Keywords:
braided bialgebras;  paired bialgebras;  twisted products;  quadratic bialgebras
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.

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