Fiber-Wise Linear Differential Operators
arXiv:2011.13192 · doi:10.1515/forum-2021-0100
Abstract
We define a new notion of fiber-wise linear differential operator on the total space of a vector bundle . Our main result is that fiber-wise linear differential operators on are equivalent to (polynomial) derivations of an appropriate line bundle over . 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.
26 pages, comments welcome!