论文标题
纤维线性差速器操作员
Fiber-Wise Linear Differential Operators
论文作者
论文摘要
我们在矢量束$ e $的总空间上定义了一个新的智能线性差速器操作员的概念。我们的主要结果是，$ e $上的光纤线性差分运算符等同于$ e^\ ast $上适当的线束的（多项式）派生。我们认为，这可能是朝着lie群体上的乘法（分别是无限的乘法）差异算子定义的第一步。我们还讨论了围绕子手机的差分运算符的线性化。
We define a new notion of fiber-wise linear differential operator on the total space of a vector bundle $E$. Our main result is that fiber-wise linear differential operators on $E$ are equivalent to (polynomial) derivations of an appropriate line bundle over $E^\ast$. We believe this might represent a first step towards a definition of multiplicative (resp. infinitesimally multiplicative) differential operators on a Lie groupoid (resp. a Lie algebroid). We also discuss the linearization of a differential operator around a submanifold.
