Abstract:

With the help of normalized integral of weak πentwined structure (A,C)π-ψ, a Maschketype theorem for weak πentwined modules is proved, that is, given a weak πentwined structure (A,C)π-ψ and supposed that there exists a normalized integral θ={θα:  Cα→Hom(Cα-1,Aα)}α∈π,then a monomorphism (resp. epimorphism) f={fα: Mα→Nα}α∈π  splits in Uπ-CA(ψ) if the monomorphism (resp. epimorphism) fe splits as an Aemodule morphism.

Key words: weak Hopf πcoalgebras, weak πentwined modules, Maschketype theorem