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arXiv · 0810.2926

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

Eivind Eriksen·Trond Stølen Gustavsen
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Abstract

Let $k$ 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.

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Eivind Eriksen, Trond Stølen Gustavsen. 2008-10-16. Lie-Rinehart cohomology and integrable connections on modules of rank one. https://arxiv.org/abs/0810.2926

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