弱Hopf群余代数的Maschke型定理

doi:10.13371/j.cnki.chin.q.j.m.2015.01.015

数学季刊 ›› 2015, Vol. 30 ›› Issue (1): 144-152.doi: 10.13371/j.cnki.chin.q.j.m.2015.01.015

弱Hopf群余代数的Maschke型定理

1. School of Mathematics and Statistics, Ludong University2. Department of Basic, Zhejiang Business College

收稿日期:2014-03-05 出版日期:2015-03-30 发布日期:2020-11-24
作者简介:JIA Ling(1974-), female, native of Yantai, Shandong, an associate professor of Ludong University, Ph.D., engages in Hopf algebra.
基金资助:
Supported by the Natural Science Foundation of Shandong Province(ZR2012AL02)；

A Maschke Type Theorem for Weak Hopf \pi-Comodules

1. School of Mathematics and Statistics, Ludong University2. Department of Basic, Zhejiang Business College

Received:2014-03-05 Online:2015-03-30 Published:2020-11-24
About author:JIA Ling(1974-), female, native of Yantai, Shandong, an associate professor of Ludong University, Ph.D., engages in Hopf algebra.
Supported by:
Supported by the Natural Science Foundation of Shandong Province(ZR2012AL02)；

摘要/Abstract

摘要： In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak（H, A）Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.

关键词: weak Hopf \pi-coalgebra, weak (H;A) Hopf \pi-comodules, Maschke type theorem

Abstract: In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak（H, A）Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.

Key words: weak Hopf \pi-coalgebra, weak (H;A) Hopf \pi-comodules, Maschke type theorem

中图分类号:

O153.3

贾玲, 陈笑缘. 弱Hopf群余代数的Maschke型定理[J]. 数学季刊, 2015, 30(1): 144-152.

JIA Ling, CHEN Xiao-yuan. A Maschke Type Theorem for Weak Hopf \pi-Comodules[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(1): 144-152.

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弱Hopf群余代数的Maschke型定理

A Maschke Type Theorem for Weak Hopf \pi-Comodules

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