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Caenepeel, S.; Janssen, K.; Wang, S. H.

Group corings. (English) Zbl 1145.16017

Appl. Categ. Struct. 16, No. 1-2, 65-96 (2008).
The authors define group corings by extending the concept of a group coalgebra, defined by Turaev, to the case where the base ring is not necessarily commutative. If \(G\) is a group and \(\mathcal C\) is a \(G\)-group coring, two concepts of \(\mathcal C\)-comodules are defined. Functors between categories of such comodules are studied, and the relationship to graded modules over graded rings is investigated. Galois group corings are defined and a structure result for \(G\)-comodules over a Galois group coring is proved. Morita contexts associated to a group coring are studied. The results are applied to group corings associated to a comodule algebra over a Hopf group coalgebra.
Reviewer: Sorin Dascalescu (Bucureşti)

Cited in 5 Reviews
Cited in 7 Documents

MSC:

16T15 Coalgebras and comodules; corings
16W50 Graded rings and modules (associative rings and algebras)
16D90 Module categories in associative algebras
16T05 Hopf algebras and their applications

Keywords:

group coalgebras; categories of comodules; Galois group corings; comodule algebras; Hopf-Galois extensions; graded rings; graded Morita contexts
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References:

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