On Weil like functors on flag vector bundles with given length-Reference-Cited by-同舟云学术

On Weil like functors on flag vector bundles with given length

Published:2023 Issue:9 Volume:37 Page:2755-2771
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Doupovec Miroslav¹,Kurek Jan²,Mikulski Włodzimierz³

Affiliation:

1. Institute of Mathematics, Brno University of Technology, FSI VUT Brno, Brno, Czech Republic

2. Institute of Mathematics, Maria Curie Sklodowska University, Lublin, Poland

3. Institute of Mathematics, Jagiellonian University, Cracow, Poland

Abstract

Let ? ? 2 be a fixed natural number. The complete description is given of the product preserving gauge bundle functors F on the category F?VB of flag vector bundles K = (K;K1,...,K?) of length ? in terms of the systems I = (I1,..., I??1) of A-module homomorphisms Ii : Vi+1 ? Vi for Weil algebras A and finite dimensional (over R) A-modules V1,...,V?. The so called iteration problem is investigated. The natural affinors on FK are classified. The gauge-natural operators C lifting ?-flag-linear (i.e. with the flow in F?VB) vector fields X on K to vector fields C(X) on FK are completely described. The concept of the complete lift F ? of a ?-flag-linear semi-basic tangent valued p-form ? on K is introduced. That the complete lift F ? preserves the Fr?licher-Nijenhuis bracket is deduced. The obtained results are applied to study prolongation and torsion of ?-flag-linear connections.

Publisher

National Library of Serbia

Subject

General Mathematics

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