Hopf algebra structure H σ - R with two sided invertible 2-cocycle

Shuan Hong Wang; Dingguo Wang

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 635-650
  • ISSN: 0010-2628

Abstract

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In this paper, we study the H σ - R type Hopf algebras and present its braided and quasitriangular Hopf algebra structure. This generalizes well-known results on H σ and H R type Hopf algebras. Finally, the classification of H σ - R type Hopf algebras is given.

How to cite

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Wang, Shuan Hong, and Wang, Dingguo. "Hopf algebra structure $H^{\sigma -R}$ with two sided invertible 2-cocycle." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 635-650. <http://eudml.org/doc/248438>.

@article{Wang1999,
abstract = {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.},
author = {Wang, Shuan Hong, Wang, Dingguo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hopf algebra; $2$-cocycle; braided Hopf algebra; bialgebras; cocycles; braided Hopf algebras; cocycle deformations},
language = {eng},
number = {4},
pages = {635-650},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hopf algebra structure $H^\{\sigma -R\}$ with two sided invertible 2-cocycle},
url = {http://eudml.org/doc/248438},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Wang, Shuan Hong
AU - Wang, Dingguo
TI - Hopf algebra structure $H^{\sigma -R}$ with two sided invertible 2-cocycle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 635
EP - 650
AB - 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.
LA - eng
KW - Hopf algebra; $2$-cocycle; braided Hopf algebra; bialgebras; cocycles; braided Hopf algebras; cocycle deformations
UR - http://eudml.org/doc/248438
ER -

References

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  2. Doi Y., Takeuchi M., Multiplication alteration by two-cocycles-The quantum version, Comm. Algebra 22 (14) (1994), 5715-5732. (1994) Zbl0821.16038MR1298746
  3. Sweelder M.E., Hopf Algebras, W.A. Benjamin, New York, 1969. MR0252485
  4. Majid S., Quasitriangular Hopf Algebras and Yang-Baxter equations, Int. J. Modern Phys. A5 (1990), 1-91. (1990) Zbl0709.17009MR1027945
  5. Montgomery S., Hopf Algebras and Their Actions on Rings, CBMS 82, Amer. Math. Soc., 1993. Zbl0793.16029MR1243637
  6. Radford D.E., On the Quasitriangular structure of a semisimple Hopf Algebras, J. Algebra 141 (2) (1991), 354-358. (1991) MR1125700
  7. I-Peng Lin B., Crossed coproducts of Hopf algebras, Comm. Algebra 10 (1) (1982), 1-17. (1982) MR0674686
  8. Reshetikhin N.Y., Multiparameter quantum groups and twisted quasi-triangular Hopf algebras, Lett. Math. Phys. 20 (1990), 331-335. (1990) MR1077966

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