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Lifting double linear vector fields to Weil like functors on double vector bundles
Author(s) -
Mikulski Włodzimierz M.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800395
Subject(s) - vector bundle , mathematics , functor , vector valued differential form , pure mathematics , gauge (firearms) , product (mathematics) , bundle , algebra over a field , normal bundle , frame bundle , geometry , materials science , archaeology , composite material , history
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 A F ‐bilinear maps⋄ F : U F × V F → W F , where A F are Weil algebras andU F , V F , W Fare finite dimensional (over R ) A F ‐modules. Then the so‐called “iteration” problem is solved (i.e. ⋄ F ′∘ Fby 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.