论文标题
Lie-Rinehart代数的通用代数包裹：交叉产品，连接和曲率
Universal enveloping algebras of Lie-Rinehart algebras: crossed products, connections, and curvature
论文作者
论文摘要
我们将最初由Blattner-Cohen-Montgomery制定的定理扩展了，用于较弱的代数对非共同代数的hopf代数产生的交叉产品，到左HOPF代数型代数。我们的主要动机是应用于普遍包裹的射射线式林哈特代数的代数：对于任何给定的弯曲（分别扁平）连接，即线性（分别为lie-rinehart）lie-rinehart代数扩展，我们提供了交叉（smash）产品分解的cross。作为一个几何示例，我们将不变矢量场在主束的总空间上产生的关联代数描述为垂直轴产生的代数的交叉产物和基座上的差分运算符的代数。
We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to universal enveloping algebras of projective Lie-Rinehart algebras: for any given curved (resp. flat) connection, that is, a linear (resp. Lie-Rinehart) splitting of a Lie-Rinehart algebra extension, we provide a crossed (resp. smash) product decomposition of the associated universal enveloping algebra, and vice versa. As a geometric example, we describe the associative algebra generated by the invariant vector fields on the total space of a principal bundle as a crossed product of the algebra generated by the vertical ones and the algebra of differential operators on the base.
