INTEGRALS AND A MASCHKE-TYPE THEOREM FOR WEAK HOPF π-COALGEBRAS

Year 2011, Volume: 10 Issue: 10, 85 - 112, 01.12.2011

Chen Quan-guo Wang Shuan-hong

Abstract

Let π be a discrete group. We shall introduce the more general
concept of an integral of a weak Doi-Hopf π-datum (H, A, C), where H is a
weak Hopf π-coalgebra coacting on an algebra A and acting on a π-coalgebra
C = {Cα}α∈π. We prove that there exists a total integral θ = {θα : Cα →
Hom(Cα−1 , A)}α∈π, then any representation of (H, A, C) is injective in a functorial
way, as a corepresentation of C and vice versa. As the application of
the existence of a total integral, we prove the Maschke-type Theorem for weak
Doi-Hopf π-modules.

Keywords

weak Hopf π-coalgebra, integral, weak Doi-Hopf π-datums