可微堆栈上的向量场和导数

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-09-16 DOI:10.1016/j.difgeo.2025.102292

Juan Sebastián Herrera-Carmona , Cristian Ortiz , James Waldron

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引用次数: 0

摘要

本文介绍并研究了李群上的乘法向量场和函数的梯度代数的模结构。我们证明了在光滑函数上的可微堆栈的向量场上存在一个适当意义上的Morita不变量的梯度Lie-Rinehart代数的关联结构。此外，我们还证明了相关的Van-Est类型映射与这些模块结构兼容。我们还提出了几个例子。

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Vector fields and derivations on differentiable stacks

We introduce and study module structures on both the dgla of multiplicative vector fields and the graded algebra of functions on Lie groupoids. We show that there is an associated structure of a graded Lie-Rinehart algebra on the vector fields of a differentiable stack over its smooth functions that is Morita invariant in an appropriate sense. Furthermore, we show that associated Van-Est type maps are compatible with those module structures. We also present several examples.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.