模余代数和Morita-Takeuchi关系

MODULE COALGEBRAS AND MORITA-TAKEUCHI CONTEXT

H是Hopf代数,C是H-模余代数。首先利用余积分的概念,诱导C的右H-余模结构,并构造了Smash余积余代数C×H,使C×H作为余代数同构于C H。然后,由C的右H-余模结构诱导C的左H0-模结构,令 C=C/KerεH0C,则C×H与 C有Morita-Takeuchi关系。

Let H be a Hopf algebra and C a H-module coalgebra.Right H-comodule structure of C is defined and a smash coproduct coalgebra C×H is constructed using the concept of cointegral.C×H and CH is isomorphismed as coalgebra.Right H-comodule structure of C induces left H^0-module structure of C,and let =C/Kerε_(H^0)C,C×H and have the Morita-Takeuchi context.