(ω,σ)-Smash积积和和(ν,α)-Smash余余积积(ω,σ)-Smash product and (ν,α)-Smash coproduct
郑乃峰;
摘要(Abstract)：
设B,H是两个Hopf代数,构造了(ω,σ)-Smash积Bω#σH和(ν,α)-Smash余积Bν■αH,并给出了Bω#σH是Hopf代数和Bν■αH是双代数的充要条件,证明了许多已知的积和余积是它们的特殊情况.
关键词(KeyWords)： Hopf代数;交叉积;Smash积;Smash余积
基金项目(Foundation): 浙江省教育厅基金(Y200906783);; 宁波市自然科学基金(2011A610172)
作者(Authors): 郑乃峰;
参考文献(References)：
- [1]Caenepeel S,Ion B,Militaru G,et al.The factorization problem and the smash biproduct of algebras andcoalgebras[J].Alg.Repr.Theory,2000,3:19-42.
- [2]Molnar R K.Semi-direct products of Hopf algebras[J].J.Algebra,1977,47:29-51.
- [3]Wang S H,Li J Q.On twisted smash products for bimodule algebras and the Drinfeld double[J].Comm.algebra,1998,26(8):2435-2444.
- [4]Drinfeld V G.Quantum groups[C]//Proceedings of the International Congress of Mathematicians.Provi-dence:Berkeley,1987.
- [5]Doi Y,Takeuchi M.Multiplication alteration by two-cocycle[J].Comm.Algebra,1994,22(14):5715-5732.
- [6]Blattner R J,Cohen M,Montgomery S.Crossed products and inner actions of Hopf algebras[J].Tran.AMS,1986,298:671-711.
- [7]Doi Y,Takeuchi M.Cleft comodule algebras of a bialgebra[J].Comm.Algebra,1986,14:801-818.
- [8]Boca I.A central theorem for Hopf algebras[J].Comm.Algebra,1997,25(8):2593-2606.
- [9]Sweedler M.Hopf Algebra[M].New York:Benjamin,1969.