Vrije Universiteit Brussel

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math.RA2005

Comatrix Corings and Galois Comodules over Firm Rings

J. Gomez-Torrecillas, J. Vercruysse

We give a notion of a comatrix coring which embodies all former constructions and, what is more interesting, leads to the formulation of a notion of Galois coring and the statement…

math.RA2005

The Brauer group of Azumaya corings and the second cohomology group

S. Caenepeel, B. Femic

Let $R$ be a commutative ring. An Azumaya coring consists of a couple $(S,\Cc)$, with $S$ a faithfully flat commutative $R$ -algebra, and an $S$ -coring $\Cc$ satisfying certain prop…

math.RA2005

Duality for finite Hopf algebras explained by corings

S. Caenepeel, D. Quinn, S. Raianu

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J.…

math.RA2005

On the cohomology of relative Hopf modules

S. Caenepeel, T. Guédénon

Let $H$ be a Hopf algebra over a field $k$ , and $A$ an $H$ -comodule algebra. The categories of comodules and relative Hopf modules are then Grothendieck categories with enough inje…

math.RA2005

Fully bounded noetherian rings and Frobenius extensions

S. Caenepeel, T. Guédénon

Let $i : A \to R$ be a ring morphism, and $χ : R \to A$ a right $R$ -linear map with $χ (χ (r) s) = χ (r s)$ and $χ (1_{R}) = 1_{A}$ . If $R$ is a Frobenius $A$ -ring, then we can define a trace map $\…

math.RA2004

The relative Picard group of a comodule algebra and Harrison cohomology

S. Caenepeel, T. Guedenon

Let $A$ be a commutative comodule algebra over a commutative bialgebra $H$ . The group of invertible relative Hopf modules maps to the Picard group of $A$ , and the kernel is describ…