Thomas Guédénon

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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…