A Maschke Type Theorem for Weak Hopf π-Comodules

陈笑缘

A Maschke Type Theorem for Weak Hopf π-Comodules

JIA Ling1, CHEN Xiao-yuan2

(1.School of Mathematics and Statistics, Ludong University, Yantai 264025, China; 2.Department of Basic, Zhejiang Business College, Hangzhou 310053, China)

　　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 π-coalgebra; weak (H,A) Hopf π-comodules; Maschke type theorem

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