Geodesic
On Weil like functors on flag vector bundles with given length
Filomat, Tome 37 (2023) no. 9, p. 2755

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DOI

Let κ ≥ 2 be a fixed natural number. The complete description is given of the product preserving gauge bundle functors F on the category F κ VB of flag vector bundles K = (K; K 1 ,. .. , K κ) of length κ in terms of the systems I = (I 1 ,. .. , I κ−1) of A-module homomorphisms I i : V i+1 → V i for Weil algebras A and finite dimensional (over R) A-modules V 1 ,. .. , V κ. The so called iteration problem is investigated. The natural affinors on FK are classified. The gauge-natural operators C lifting κ-flag-linear (i.e. with the flow in F κ VB) vector fields X on K to vector fields C(X) on FK are completely described. The concept of the complete lift F φ of a κ-flag-linear semi-basic tangent valued p-form φ on K is introduced. That the complete lift F φ preserves the Frölicher-Nijenhuis bracket is deduced. The obtained results are applied to study prolongation and torsion of κ-flag-linear connections.
DOI : 10.2298/FIL2309755D
Classification : 58A05, 58A20, 58A32
Keywords: product preserving gauge bundle functor, natural transformation, Weil algebra, flag-linear vector bundle, flag-linear semi-basic tangent valued p-form, complete lifting, Frölicher-Nijenhuis bracket, flag-linear connection 
Miroslav Doupovec; Jan Kurek; Włodzimierz M Mikulski. On Weil like functors on flag vector bundles with given length. Filomat, Tome 37 (2023) no. 9, p. 2755 . doi: 10.2298/FIL2309755D
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     author = {Miroslav Doupovec and Jan Kurek and W{\l}odzimierz M Mikulski},
     title = {On {Weil} like functors on flag vector bundles with given length},
     journal = {Filomat},
     pages = {2755 },
     year = {2023},
     volume = {37},
     number = {9},
     doi = {10.2298/FIL2309755D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309755D/}
}
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