## Liftings of linear vector fields to product preserving gauge bundle functors on vector bundles.(English)Zbl 1026.58003

Let $$F$$ be a product preserving gauge bundle functor defined on the category of vector bundles. The authors classify all natural operators transforming linear vector fields on a vector bundle $$Y$$ to vector fields on $$FY$$. The classification is given as a sum of generalized flow operators and absolute operators.

### MSC:

 58A32 Natural bundles 53A55 Differential invariants (local theory), geometric objects 22E60 Lie algebras of Lie groups

### Keywords:

lifting; product preserving functor; vector bundle; Weil module
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