Fiberwise linear differential operators

被引：1

作者：

Pugliese, Fabrizio ^{[1
]}

Sparano, Giovanni ^{[1
]}

Vitagliano, Luca ^{[1
]}

机构：

[1] Univ Salerno, DipMat, Via Giovanni Paolo II 123, I-84084 Fisciano, SA, Italy

来源：

FORUM MATHEMATICUM | 2021年 / 33卷 / 06期

关键词：

Vector bundles; differential operators; Lie algebroids; multivectors;

D O I：

10.1515/forum-2021-0100

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a new notion of fiberwise linear differential operator on the total space of a vector bundle E. Our main result is that fiberwise linear differential operators on E are equivalent to (polynomial) derivations of an appropriate line bundle over E*. 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.

引用

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页码：1445 / 1469

页数：25

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