论文标题
在Lie-rinehart代数的绳索上
On sheaves of Lie-Rinehart algebras
论文作者
论文摘要
我们研究了局部环形空间上的Lie-rinehart代数的滑轮。我们介绍了这种或骨的形态和合并症，并证明了每种形态的分解定理。使用这种形态的概念，我们获得了（较高的）同型组和类固醇，以直接概括为同型基团和lie代数的Weinstein groupoids。我们认为，在光滑的歧管上，Lie-rinehart代数的系带皮带的特殊情况。我们表明，在某些合理的假设下，这种滑轮会诱导基础歧管的隔离叶片，而这些叶子恰恰是基本群的轨道。
We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher) homotopy groups and groupoids for such objects which directly generalize the homotopy groups and Weinstein groupoids of Lie algebroids. We consider, the special case of sheaves of Lie-Rinehart algebras over smooth manifolds. We show that, under some reasonable assumptions, such sheaves induce a partition of the underlying manifold into leaves and that these leaves are precisely the orbits of the fundamental groupoid.
