Lie-Rinehart cohomology and integrable connections on modules of rank one - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: Let $k$ be an algebraically closed field of characteristic 0, let $R$ be acommutative $k$-algebra, and let $M$ be a torsion free $R$-module of rank onewith a connection $ abla$. We consider the Lie-Rinehart cohomology with valuesin $End {R}M$ with its induced connection, and give an interpretation of thiscohomology in terms of the integrable connections on $M$. When $R$ is anisolated singularity of dimension $d\geq2$, we relate the Lie-Rinehartcohomology to the topological cohomology of the link of the singularity, andwhen $R$ is a quasi-homogenous hypersurface of dimension two, we give acomplete computation of the cohomology.



Author: Eivind Eriksen, Trond Stølen Gustavsen

Source: https://arxiv.org/



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