| Title:
|
Hopf algebra structure $H^{\sigma-R}$ with two sided invertible 2-cocycle (English) |
| Author:
|
Wang, Shuanhong |
| Author:
|
Wang, Dingguo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
635-650 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the $H^{\sigma-R}$ type Hopf algebras and present its braided and quasitriangular Hopf algebra structure. This generalizes well-known results on $H^{\sigma }$ and $H^R$ type Hopf algebras. Finally, the classification of $H^{\sigma -R}$ type Hopf algebras is given. (English) |
| Keyword:
|
Hopf algebra |
| Keyword:
|
$2$-cocycle |
| Keyword:
|
braided Hopf algebra |
| MSC:
|
16W30 |
| MSC:
|
81R50 |
| idZBL:
|
Zbl 1014.16038 |
| idMR:
|
MR1756542 |
| . |
| Date available:
|
2009-01-08T18:56:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119120 |
| . |
| Reference:
|
[1] Doi Y.: Braided bialgebras and quadratic bialgebras.Comm. Algebra 21 (5) (1993), 1731-1749. Zbl 0779.16015, MR 1213985 |
| Reference:
|
[2] Doi Y., Takeuchi M.: Multiplication alteration by two-cocycles-The quantum version.Comm. Algebra 22 (14) (1994), 5715-5732. Zbl 0821.16038, MR 1298746 |
| Reference:
|
[3] Sweelder M.E.: Hopf Algebras.W.A. Benjamin, New York, 1969. MR 0252485 |
| Reference:
|
[4] Majid S.: Quasitriangular Hopf Algebras and Yang-Baxter equations.Int. J. Modern Phys. A5 (1990), 1-91. Zbl 0709.17009, MR 1027945 |
| Reference:
|
[5] Montgomery S.: Hopf Algebras and Their Actions on Rings.CBMS 82, Amer. Math. Soc., 1993. Zbl 0793.16029, MR 1243637 |
| Reference:
|
[6] Radford D.E.: On the Quasitriangular structure of a semisimple Hopf Algebras.J. Algebra 141 (2) (1991), 354-358. MR 1125700 |
| Reference:
|
[7] I-Peng Lin B.: Crossed coproducts of Hopf algebras.Comm. Algebra 10 (1) (1982), 1-17. MR 0674686 |
| Reference:
|
[8] Reshetikhin N.Y.: Multiparameter quantum groups and twisted quasi-triangular Hopf algebras.Lett. Math. Phys. 20 (1990), 331-335. MR 1077966 |
| . |
