Lifting double linear vector fields to Weil like functors on double vector bundles

Włodzimierz M. Mikulski

Mathematische Nachrichten, 2019, vol. 292, issue 9, 2092-2100

Abstract: The complete description is given of the product preserving gauge bundle functors F on the category 2−VB of double vector bundles in terms of the AF‐bilinear maps ⋄F:UF×VF→WF, where AF are Weil algebras and UF,VF,WF are finite dimensional (over R) AF‐modules. Then the so‐called “iteration” problem is solved (i.e. ⋄F′∘F by means of ⋄F and ⋄F′ is computed). That any two product preserving gauge bundle functors on 2−VB commute is derived. All gauge natural operators lifting double linear vector fields to product preserving gauge bundle functors F are completely described.

Date: 2019
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https://doi.org/10.1002/mana.201800395

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