Detail publikace

On Weil like functors on flag vector bundles with given length

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

Anglický název

On Weil like functors on flag vector bundles with given length

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

31.03.2023

Nakladatel

Faculty of Sciences and Mathematics, University of Niš, Serbia

Místo

Serbia

ISSN

0354-5180

Ročník

37

Číslo

9

Strany od–do

2755–2771

Počet stran

17

BIBTEX


@article{BUT183286,
  author="Miroslav {Doupovec} and Jan {Kurek} and Wlodzimierz {Mikulski},
  title="On Weil like functors on flag vector bundles with given length",
  year="2023",
  volume="37",
  number="9",
  month="March",
  pages="2755--2771",
  publisher="Faculty of Sciences and Mathematics, University of Niš, Serbia",
  address="Serbia",
  issn="0354-5180"
}