Detail publikačního výsledku

On Weil like functors on flag vector bundles with given length

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

Original Title

On Weil like functors on flag vector bundles with given length

English Title

On Weil like functors on flag vector bundles with given length

Type

WoS Article

Original Abstract

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

English abstract

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

Keywords

product preserving gauge bundle functor;natural transformation;Weil algebra;flag-linear vector bundle;flag-linear semi-basic tangent valued p-form;complete lifting;Fro?licher-Nijenhuis bracket;flag-linear connection

Key words in English

product preserving gauge bundle functor;natural transformation;Weil algebra;flag-linear vector bundle;flag-linear semi-basic tangent valued p-form;complete lifting;Fro?licher-Nijenhuis bracket;flag-linear connection

Authors

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

RIV year

2024

Released

31.03.2023

Publisher

Faculty of Sciences and Mathematics, University of Niš, Serbia

Location

Serbia

ISBN

0354-5180

Periodical

Filomat

Volume

37

Number

9

State

Republic of Serbia

Pages from

2755

Pages to

2771

Pages count

17

URL

https://www.pmf.ni.ac.rs/filomat-content/2023/37-9/37-9-9-18390.pdf

Full text in the Digital Library

http://hdl.handle.net/

BibTex

@article{BUT183286,
  author="Miroslav {Doupovec} and Jan {Kurek} and Wlodzimierz {Mikulski}",
  title="On Weil like functors on flag vector bundles with given length",
  journal="Filomat",
  year="2023",
  volume="37",
  number="9",
  pages="2755--2771",
  doi="10.2298/FIL2309755D",
  issn="0354-5180",
  url="https://www.pmf.ni.ac.rs/filomat-content/2023/37-9/37-9-9-18390.pdf"
}