Acta mathematica scientia,Series A

• Articles • Previous Articles     Next Articles

Weak Skew Paired Bialgebras and Weak Relative Long Bialgebras

Zhang Liangyun   

  1. College of Science, Nanjing Agricultural University, Nanjing 210095
  • Received:2004-12-30 Revised:2006-03-10 Online:2006-08-25 Published:2006-08-25
  • Contact: Zhang Liangyun

Abstract: This paper gives a sufficient and
necessary condition for given twisted product
(Hσ,σ) to be a weak bialgebra. If [B,H,τ] are weak skew paired bialgebras and τ is invertible,
then, under some condition, the weak
bicrossed product BτH is a weak bialgebra. If (B,H,σ) is a weak relative Long bialgebra and σ
invertible, then the weak bicrossed product BOPσH can be constructed. Espically, for the Sweedler 4-dimensional
Hopf algebra H4, the author gives an example to show that
(BOPσH4,β) is not only a Long bialgebra
but also a non-commutative and non-cocommutative 8-dimensional
Hopf algebra, where B is a sub-Hopf algebra of H4. If B and
H are weak bialgebras, and σ:BHk is
a linear map, then a sufficient and necessary condition
for (B,σ,,ΔB) to be a weak right
relative (H,B)-dimodule algebra is given.

Key words: Weak skew paired bialgebra, Weak bicrossed product, Weak relative long bialgebra, Weak relative dimodule algebra

CLC Number: 

  • 16W30
Trendmd