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

Autor:	Eriksen, Eivind, Gustavsen, Trond Stølen
Rok vydání:	2008
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0810.2926 Zobrazit plný text záznamu View this record from Arxiv