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arXiv · 2011.13192

Fiber-Wise Linear Differential Operators

Fabrizio Pugliese·Giovanni Sparano·Luca Vitagliano
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Abstract

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.

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Fabrizio Pugliese, Giovanni Sparano, Luca Vitagliano. 2020-11-26. Fiber-Wise Linear Differential Operators. https://doi.org/10.1515/forum-2021-0100

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