Acta mathematica scientia,Series A
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Zhang Liangyun
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Abstract: This paper gives a sufficient andnecessary 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 weakbicrossed product B⋈τH is a weak bialgebra. If (B,H,σ) is a weak relative Long bialgebra and σinvertible, then the weak bicrossed product BOP⋈σH can be constructed. Espically, for the Sweedler 4-dimensionalHopf algebra H4, the author gives an example to show that(BOP⋈σH4,β) is not only a Long bialgebrabut also a non-commutative and non-cocommutative 8-dimensionalHopf algebra, where B is a sub-Hopf algebra of H4. If B andH are weak bialgebras, and σ:B⊗H→k isa linear map, then a sufficient and necessary conditionfor (B,σ,↼,ΔB) to be a weak rightrelative (H,B)-dimodule algebra is given.
Key words: Weak skew paired bialgebra, Weak bicrossed product, Weak relative long bialgebra, Weak relative dimodule algebra
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Zhang Liangyun. Weak Skew Paired Bialgebras and Weak Relative Long Bialgebras[J].Acta mathematica scientia,Series A, 2006, 26(4): 601-611.
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http://121.43.60.238/sxwlxbA/EN/Y2006/V26/I4/601
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