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

Authors : Chen Quanguo, Wang Shuanhong

Pages : 85-112

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Publication Date : 2011-12-01

Article Type : Research Paper

Abstract :Let π be a discrete group. We shall introduce the more general concept of an integral of a weak Doi-Hopf π-datum insert ignore into journalissuearticles values(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 → Hominsert ignore into journalissuearticles values(Cα−1 , A);}α∈π, then any representation of insert ignore into journalissuearticles values(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