弱Hopf代数上的Smash双积(英文)

Smash Biproduct Over Weak Hopf Algebras

设B,H是弱Hopf代数,ω:BH→HB和v:HB→BH是两个线性映射,我们构造了一个ω-smash积B#_ωH,一个v-smash余积B_v■H和一个(ω,v)-smash双积B_v■_ωH,同时我们给出了使B#_ωH,B_v■H,B_v■_ωH是弱Hopf代数的充分条件.我们构造的双积推广了由Caenepeel,Ion,Militaru和Zhu所构造的Smash双积.

Let B,H be weak Hopf algebras.We consider two linear mapsω：B H→H B and v：H B→BH and introduce anω-smash product B#_ωH,an v-smash coproduct Bv H and an（ω,v）-smash biproduct BvωH.Sufficient conditions for B#ωH,Bv H,BvωH to be weak Hopf algebras are also given.Our construction generalizes smash biproduct introduced by Caenepeel,Ion,Militaru and Zhu.