Homogeneous algebraic distributions

Let p:E→M be a vector bundle of dimension n+m and (xλ,yi), λ=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the type X=∑mi=1Pi∂/∂yi, where Pi are polynomials [respective...

Descripción completa

Detalles Bibliográficos
Autores: Castrillón López, Marco, Muñoz Masqué, Jaime
Tipo de recurso: artículo
Fecha de publicación:2001
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/58902
Acceso en línea:https://hdl.handle.net/20.500.14352/58902
Access Level:acceso abierto
Palabra clave:514.7
Adjoint bundle
algebraic morphism of vector bundles
algebraic vector field
involutive distribution
gauge algebra
linear representation
Lie group bundle
Liouville's vector field.
Geometría diferencial
1204.04 Geometría Diferencial
id ES_7e83ca7eb297665bcd3da01aef5672d3
oai_identifier_str oai:docta.ucm.es:20.500.14352/58902
network_acronym_str ES
network_name_str España
repository_id_str
spelling Homogeneous algebraic distributionsCastrillón López, MarcoMuñoz Masqué, Jaime514.7Adjoint bundlealgebraic morphism of vector bundlesalgebraic vector fieldinvolutive distributiongauge algebralinear representationLie group bundleLiouville's vector field.Geometría diferencial1204.04 Geometría DiferencialLet p:E→M be a vector bundle of dimension n+m and (xλ,yi), λ=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the type X=∑mi=1Pi∂/∂yi, where Pi are polynomials [respectively, homogeneous polynomials of degree d] in coordinates yi. A vertical distribution over E is said to be algebraic [respectively, homogeneous algebraic of degree d] if all local generators are homogeneous algebraic [respectively, homogeneous algebraic of the same degree d] vector fields. It is proved that a vertical distribution locally spanned by vector fields X1,…,Xr is homogeneous algebraic of degree d if and only if an r×r matrix A=(aij), aij∈C∞(E), exists which is equal to d−1 times the identity matrix along the zero section of E, and such that [χ,Xj]=∑ri=1aijXi, j=1,…,r, where χ is the Liouville vector field.Rocky Mountain Mathematics ConsortiumUniversidad Complutense de Madrid20012001-01-0120012001-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/58902reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/589022026-06-02T12:44:21Z
dc.title.none.fl_str_mv Homogeneous algebraic distributions
title Homogeneous algebraic distributions
spellingShingle Homogeneous algebraic distributions
Castrillón López, Marco
514.7
Adjoint bundle
algebraic morphism of vector bundles
algebraic vector field
involutive distribution
gauge algebra
linear representation
Lie group bundle
Liouville's vector field.
Geometría diferencial
1204.04 Geometría Diferencial
title_short Homogeneous algebraic distributions
title_full Homogeneous algebraic distributions
title_fullStr Homogeneous algebraic distributions
title_full_unstemmed Homogeneous algebraic distributions
title_sort Homogeneous algebraic distributions
dc.creator.none.fl_str_mv Castrillón López, Marco
Muñoz Masqué, Jaime
author Castrillón López, Marco
author_facet Castrillón López, Marco
Muñoz Masqué, Jaime
author_role author
author2 Muñoz Masqué, Jaime
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 514.7
Adjoint bundle
algebraic morphism of vector bundles
algebraic vector field
involutive distribution
gauge algebra
linear representation
Lie group bundle
Liouville's vector field.
Geometría diferencial
1204.04 Geometría Diferencial
topic 514.7
Adjoint bundle
algebraic morphism of vector bundles
algebraic vector field
involutive distribution
gauge algebra
linear representation
Lie group bundle
Liouville's vector field.
Geometría diferencial
1204.04 Geometría Diferencial
description Let p:E→M be a vector bundle of dimension n+m and (xλ,yi), λ=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the type X=∑mi=1Pi∂/∂yi, where Pi are polynomials [respectively, homogeneous polynomials of degree d] in coordinates yi. A vertical distribution over E is said to be algebraic [respectively, homogeneous algebraic of degree d] if all local generators are homogeneous algebraic [respectively, homogeneous algebraic of the same degree d] vector fields. It is proved that a vertical distribution locally spanned by vector fields X1,…,Xr is homogeneous algebraic of degree d if and only if an r×r matrix A=(aij), aij∈C∞(E), exists which is equal to d−1 times the identity matrix along the zero section of E, and such that [χ,Xj]=∑ri=1aijXi, j=1,…,r, where χ is the Liouville vector field.
publishDate 2001
dc.date.none.fl_str_mv 2001
2001-01-01
2001
2001-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/58902
url https://hdl.handle.net/20.500.14352/58902
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Rocky Mountain Mathematics Consortium
publisher.none.fl_str_mv Rocky Mountain Mathematics Consortium
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869411741521149952
score 15,300719

Similares en LA Referencia