Lie-Rinehart cohomology and integrable connections on modules of rank one

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dc.creatorEriksen, Eivind
dc.creatorGustavsen, Trond Stølen
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:40Z
dc.date.available2026-07-07T10:10:40Z
dc.descriptionLet $k$ be an algebraically closed field of characteristic 0, let $R$ be a commutative $k$-algebra, and let $M$ be a torsion free $R$-module of rank one with a connection $\nabla$. We consider the Lie-Rinehart cohomology with values in $End_{R}(M)$ with its induced connection, and give an interpretation of this cohomology in terms of the integrable connections on $M$. When $R$ is an isolated singularity of dimension $d\geq2$, we relate the Lie-Rinehart cohomology to the topological cohomology of the link of the singularity, and when $R$ is a quasi-homogenous hypersurface of dimension two, we give a complete computation of the cohomology.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/0810.2926
dc.identifierhttp://arxiv.org/abs/0810.2926
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171661
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectRepresentation Theory
dc.titleLie-Rinehart cohomology and integrable connections on modules of rank one
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