Descent Cohomology and Corings
@article{Brzezinski2006DescentCA, title={Descent Cohomology and Corings}, author={Tomasz Brzezinski}, journal={Communications in Algebra}, year={2006}, volume={36}, pages={1894 - 1900} }
A coring approach to non-Abelian descent cohomology of Nuss and Wambst (2007) is described and a definition of a Galois cohomology for partial group actions is proposed.
8 Citations
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In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The…
A Bicategorical Version of Masuoka’s Theorem
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We give a bicategorical version of the main result of Masuoka (Tsukuba J Math 13:353–362, 1989) which proposes a non-commutative version of the fact that for a faithfully flat extension of…
On the set of grouplikes of a coring
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We focus our attention to the set Gr(ℭ) of grouplike elements of a coring ℭ over a ring A. We do some observations on the actions of the groups U(A) and Aut(ℭ) of units of A and of automorphisms of…
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We give an overview of publications on partial actions and related concepts, paying main attention to some recent developments on diverse aspects of the theory, such as partial actions of semigroups,…
Partial actions: a survey
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We give a short survey on partial actions, partial representations and related notions. In the theory of C ∗ -algebras a concept of a partial action was introduced as an efficient tool of their…
References
SHOWING 1-10 OF 20 REFERENCES
Galois corings from the descent theory point of view
- Mathematics
- 2003
We introduce Galois corings, and give a survey of properties that have been obtained so far. The Definition is motivated using descent theory, and we show that classical Galois theory, Hopf-Galois…
Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings
- Mathematics
- 2002
Abstract.We study the corings whose category of right comodules has a finitely generated projective generator. In order to extricate the structure of these corings, we introduce the notion of…
Galois corings applied to partial Galois theory
- Mathematics
- 2004
Partial Galois extensions were recently introduced by Dokuchaev, Ferrero and Paques. We introduce partial Galois extensions for noncommutative rings, using the theory of Galois corings. We associate…
Corings and Comodules
- Mathematics
- 2003
Preface Notations 1. Coalgebras and comodules 2. Bialgebras and hopf algebras 3. Corings and comodules 4. Corings and extensions of rings 5. Corings and entwining structures 6. Weak corings and…
Comatrix Corings and Galois Comodules over Firm Rings
- Mathematics
- 2005
We construct comatrix corings on bimodules without finiteness conditions by using firm rings. This leads to the formulion of a notion of Galois coring which plays a key role in the statement of a…
The Structure of Corings: Induction Functors, Maschke-Type Theorem, and Frobenius and Galois-Type Properties
- Mathematics
- 2000
Given a ring A and an A-coring C, we study when the forgetful functor from the category of right C-comodules to the category of right A-modules and its right adjoint −⊗AC are separable. We then…
Infinite comatrix corings
- Mathematics
- 2004
We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (noncommutative) descent theory. In order to extricate the structure of…
Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties
- Mathematics, Computer Science
- 2004
An affineness criterion is proved in the situation where the coring is coseparable, and a new version of the Joyal-Tierney Descent Theorem is proved, and the Galois Coring structure theorem is generalized.