Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 2: 293 - 308

DOI: https://doi.org/10.1007/s11464-011-0096-y

RESEARCH ARTICLE

A class of new braided Hopf algebras

  • Tianshui MA , 1 ,
  • Haiying LI 1 ,
  • Shuanhong WANG 2
Expand
  • 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
  • 2. Department of Mathematics, Southeast University, Nanjing 211189, China

Received date: 15 Jan 2010

Accepted date: 09 Nov 2010

Published date: 01 Apr 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

We give the necessary and sufficient conditions for a general crossed product algebra equipped with the usual tensor product coalgebra structure to be a Hopf algebra. Furthermore, we obtain the necessary and sufficient conditions for the general crossed product Hopf algebra to be a braided Hopf algebra which generalizes some known results.

Key words： Crossed product; braided Hopf algebra; twisted product

Cite this article

Tianshui MA , Haiying LI , Shuanhong WANG . A class of new braided Hopf algebras[J]. Frontiers of Mathematics in China, 2011 , 6(2) : 293 -308 . DOI: 10.1007/s11464-011-0096-y

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Beattie M, Bulacu D. Braided Hopf algebras obtained from coquasitriangular Hopf algebra. Commun Math Phys, 2008, 282: 115-160

DOI

2
Blattner R J, Cohen M, Montgomery S. Crossed products and inner actions of Hopf algebras. Trans AMS, 1986, 289: 671-711

DOI

3
Brzeziński T. Crossed products by a coalgebra. Comm Algebra, 1997, 25: 3551-3575

DOI

4
Caenepeel S, Ion B, Militaru G, Zhu S. The factorization problem and the smash biproduct of algebras and coalgebras. Algebra Represent Theory, 2000, 3: 19-42

DOI

5
Doi Y. Braided bialgebras and quadratic bialgebras. Comm Algebra, 1993, 21(5): 1731-1749

DOI

6
Doi Y, Takeuchi M. Cleft comodule algebras for a bialgebra. Comm Algebra, 1986, 14: 801-818

DOI

7
Doi Y, Takeuchi M, Multiplication alteration by two-cocycles—The quantum version. Comm Algebra, 1994, 22: 5715-5732

DOI

8
Larson R, Towber J. Two dual classes of bialgebras related to the concepts of “quantum groups” and “quantum Lie algebras”. Comm Algebra, 1991, 19: 3295-3345

DOI

9
Molnar R K. Semi-direct products of Hopf algebras. J Algebra, 1977, 47: 29-51

DOI

10
Montgomery S. Hopf Algebras and Their Actions on Rings. CBMS Lectures in Math, Vol 82. Providence: AMS, 1993

11
Sweedler M E. Hopf Algebras. New York: Benjamin, 1969

12
Wang S H. On braided Hopf algebra structures over the twisted smash products. Comm Algebra, 1999, 27: 5561-5573

DOI

13
Wang S H, Li J Q. On the twisted smash product for bimodule algebras and Drinfel’d double. Comm Algebra, 1998, 26: 2435-2444

DOI

Options
Outlines

/

〈 〉