Pseudodifferential operators on differential groupoids
Pseudodifferential operators on differential groupoids
复制标题
DOI：
10.2140/pjm.1999.189.117
复制
发表时间：
1997-02
影响因子：
0.6
通讯作者：
V. Nistor;A. Weinstein;P. Xu
中科院分区：
文献类型：
--
作者：
V. Nistor;A. Weinstein;P. Xu
我们构造了一个伪微分算子代数，该代数对可微群类进行了推广，使其允许有角的流形。我们展示了这个结构包含了许多例子。正则算子的子代数在非交换几何意义上等价于群拟的光滑代数。我们代数的符号演算是群拟李代数对偶上函数的泊松代数。作为应用，我们给出了李代数的poincarebirkhofft - witt定理的一个新的证明，并给出了李代数对偶a *上Lie- poisson结构的一个具体量化。
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of regularizing operators is identified with the smooth algebra of the groupoid, in the sense of non-commutative geometry. Symbol calculus for our algebra lies in the Poisson algebra of functions on the dual of the Lie algebroid of the groupoid. As applications, we give a new proof of the PoincareBirkhoff-Witt theorem for Lie algebroids and a concrete quantization of the Lie-Poisson structure on the dual A∗ of a Lie algebroid.