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2013•Communications in AlgebraRequires access

Doi–Hopf Modules Associated to Comodule Coalgebras

S. Dǎscǎlescu, C. Năstăsescu, Bogdan Toader

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Abstract

To any right comodule coalgebra C over a Hopf algebra H we associate a left H-comodule algebra A. Under certain conditions, in particular in the case where H has nonzero integrals, we show that the category of right C, H-comodules is isomorphic to a certain subcategory of the category of Doi–Hopf modules associated to A. As an application, we investigate the connection between C and the smash coproduct C ⋊ H being right semiperfect.

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What this paper is about

To any right comodule coalgebra C over a Hopf algebra H we associate a left H-comodule algebra A. Under certain conditions, in particular in the case where H has nonzero integrals, we show that the category of right C, H-comodules is isomorphic to a certain subcategory of the category of Doi–Hopf modules associated to A. As an application, we investigate the connection between C and the smash coproduct C ⋊ H being right semiperfect.

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Available abstract

To any right comodule coalgebra C over a Hopf algebra H we associate a left H-comodule algebra A. Under certain conditions, in particular in the case where H has nonzero integrals, we show that the category of right C, H-comodules is isomorphic to a certain subcategory of the category of Doi–Hopf modules associated to A. As an application, we investigate the connection between C and the smash coproduct C ⋊ H being right semiperfect.

Key concepts: Hopf algebra, Mathematics, Coalgebra, Coproduct, Quasitriangular Hopf algebra, Pure mathematics, Subcategory, Representation theory of Hopf algebras

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