Journal of Lie Theory 35 (2025), No. 3, 583--591
Copyright Heldermann Verlag 2025
Differential Operators and Infinitesimally Equivariant Bundles
Emile Bouaziz
Institute of Mathematics, Academia Sinica, Taipei City, Taiwan
emile.g.bouaziz@gmail.com
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.
Keywords: Lie algebras of vector fields, differential operators.
MSC: 17B65, 14F10, 14B10.
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