The relative Picard group of a comodule algebra and Harrison cohomology

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dc.creatorCaenepeel, S.
dc.creatorGuedenon, T.
dc.date2004-10-07
dc.date.accessioned2026-07-07T05:13:03Z
dc.date.available2026-07-07T05:13:03Z
dc.descriptionLet $A$ 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 described as a quotient group of the group of invertible grouplike elements of the coring $A\ot H$, or as a Harrison cohomology group. Our methods are based on elementary $K$-theory. The Hilbert 90 Theorem follows as a corollary. The part of the Picard group of the coinvariants that becomes trivial after base extension embeds in the Harrison cohomology group, and the image is contained in a well-defined subgroup $E$. It equals $E$ if $H$ is a cosemisimple Hopf algebra over a field.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0410209
dc.identifierhttp://arxiv.org/abs/math/0410209
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72804
dc.subjectRings and Algebras
dc.subject16W30
dc.titleThe relative Picard group of a comodule algebra and Harrison cohomology
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