Journal of Lie Theory

no. 3
Differential Operators and Infinitesimally Equivariant Bundles
Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 583-591
We study AV-modules, as in the work of Billig and collaborators, from a more geometric perspective. We show that if the underlying sheaf is a vector bundle, then the covariant derivative by a vector field depends almost O-linearly on the vector field. More precisely, we will show that a certain Lie map is a differential operator. This strengthens a theorem of the author and Rocha, in the sense that the bound on the order of a certain differential operator is improved upon quadratically.
DOI: 10.5802/jolt.1398
Classification: 17B65, 14F10, 14B10
Keywords: Lie algebras of vector fields, differential operators 
@article{JOLT_2025_35_3_a6,
     author = {E. Bouaziz},
     title = {Differential {Operators} and {Infinitesimally} {Equivariant} {Bundles}},
     journal = {Journal of Lie Theory},
     pages = {583--591},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1398},
     zbl = {08103103},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1398/}
}
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E. Bouaziz. Differential Operators and Infinitesimally Equivariant Bundles. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 583-591. doi: 10.5802/jolt.1398

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