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2012•Journal of Algebra and Its ApplicationsRequires access

ON COREPRESENTATION OF HOPF π-COALGEBRAS

Quanguo Chen, Dingguo Wang, BAITAKAZI NUERDANBIEKE

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Abstract

Let π be a group and H be a Hopf π-coalgebra. We investigate the criterion for the existence of a total integral of π-H-comodule algebra A in the setting of Hopf π-coalgebras, and prove that there exists a total integral θ = {θα : Hα → A} if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of H, which generalizes the result invented by Doi in the ordinary Hopf algebra setting.

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Let π be a group and H be a Hopf π-coalgebra. We investigate the criterion for the existence of a total integral of π-H-comodule algebra A in the setting of Hopf π-coalgebras, and prove that there exists a total integral θ = {θα : Hα → A} if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of H, which generalizes the result invented by Doi in the ordinary Hopf algebra setting.

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Available abstract

Let π be a group and H be a Hopf π-coalgebra. We investigate the criterion for the existence of a total integral of π-H-comodule algebra A in the setting of Hopf π-coalgebras, and prove that there exists a total integral θ = {θα : Hα → A} if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of H, which generalizes the result invented by Doi in the ordinary Hopf algebra setting.

Key concepts: Hopf algebra, Mathematics, Coalgebra, Injective function, Quasitriangular Hopf algebra, Representation theory of Hopf algebras, Pure mathematics, Quantum group

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