# Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Extracta Mathematicae (2006)

- Volume: 21, Issue: 3, page 273-286
- ISSN: 0213-8743

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topMikulski, Wlodzimierz M.. "Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.." Extracta Mathematicae 21.3 (2006): 273-286. <http://eudml.org/doc/41865>.

@article{Mikulski2006,

abstract = {Let A be a Weil algebra and V be an A-module with dimR V < ∞. Let E → M be a vector bundle and let TA,VE → TAM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form TA,Vφ : TA,V E → ΛpT*TAM ⊗TAM TTA,VE on TA,VE → TAM from a linear semibasic tangent valued p-form φ : E → ΛpT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vφ, TA,Vψ]] = TA,V ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply these results to linear general connections on E → M.},

author = {Mikulski, Wlodzimierz M.},

journal = {Extracta Mathematicae},

keywords = {Variedades diferenciables; Haces vectoriales; Functores; linear semibasic tangent valued form; Weil algebra; gauge bundle functor; Frolicher-Nijenhuis bracket; generalized Weil bundle; canonical affinor},

language = {eng},

number = {3},

pages = {273-286},

title = {Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.},

url = {http://eudml.org/doc/41865},

volume = {21},

year = {2006},

}

TY - JOUR

AU - Mikulski, Wlodzimierz M.

TI - Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

JO - Extracta Mathematicae

PY - 2006

VL - 21

IS - 3

SP - 273

EP - 286

AB - Let A be a Weil algebra and V be an A-module with dimR V < ∞. Let E → M be a vector bundle and let TA,VE → TAM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form TA,Vφ : TA,V E → ΛpT*TAM ⊗TAM TTA,VE on TA,VE → TAM from a linear semibasic tangent valued p-form φ : E → ΛpT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[TA,Vφ, TA,Vψ]] = TA,V ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply these results to linear general connections on E → M.

LA - eng

KW - Variedades diferenciables; Haces vectoriales; Functores; linear semibasic tangent valued form; Weil algebra; gauge bundle functor; Frolicher-Nijenhuis bracket; generalized Weil bundle; canonical affinor

UR - http://eudml.org/doc/41865

ER -

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