π-H-模余代数的Morita-Takeuchi关系

The Morita-Takeuchi context of π-H-module coalgebras

设π为有限群,H为有限型Hopfπ-余代数,C为左π-H-模余代数.利用π-余积分诱导出C的右π-H-余模结构,并构造了π-分次余代数C×H;再由C的右π-H-余模结构诱导出C的左H*-模结构;最后利用π-群象元素和π-积分建立了C×H与C=C/(H*+.C)之间的Morita-Takeuchi关系.

Let π be a finite group and H a finite type Hopf π-coalgebras over a field K,C a left π-H-module coalgebra.Right π-H-comodule structure of C and π-graded coalgebra C×H~ were defined by π-cointegral.Then,right π-H-comodule structure of C induced left H＊-module structure of C.A Morita-Takeuchi context between C×H~ and C-=C/（H＊＋·C） was constructed by π-grouplike elements and π-integrals.