Integrable systems on semidirect product Lie groups

Autores
Capriotti, Santiago; Montani, Hugo Santos
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler–Kostant–Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson–Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.
Fil: Capriotti, Santiago. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Montani, Hugo Santos. Universidad Nacional de la Patagonia Austral. Unidad Académica Caleta Olivia. Departamento de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Integrable Systems
Adler–Kostant–Symes Method
Semidirect Product Lie Algebras
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/21691
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Integrable systems on semidirect product Lie groupsCapriotti, SantiagoMontani, Hugo SantosIntegrable SystemsAdler–Kostant–Symes MethodSemidirect Product Lie Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler–Kostant–Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson–Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.Fil: Capriotti, Santiago. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Montani, Hugo Santos. Universidad Nacional de la Patagonia Austral. Unidad Académica Caleta Olivia. Departamento de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaIOP Publishing2014-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/21691Capriotti, Santiago; Montani, Hugo Santos; Integrable systems on semidirect product Lie groups; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 47; 206; 5-2014; 1-231751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/47/20/205206/info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/47/20/205206info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:09Zoai:ri.conicet.gov.ar:11336/21691instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:18:09.245CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Integrable systems on semidirect product Lie groups
title Integrable systems on semidirect product Lie groups
spellingShingle Integrable systems on semidirect product Lie groups
Capriotti, Santiago
Integrable Systems
Adler–Kostant–Symes Method
Semidirect Product Lie Algebras
title_short Integrable systems on semidirect product Lie groups
title_full Integrable systems on semidirect product Lie groups
title_fullStr Integrable systems on semidirect product Lie groups
title_full_unstemmed Integrable systems on semidirect product Lie groups
title_sort Integrable systems on semidirect product Lie groups
dc.creator.none.fl_str_mv Capriotti, Santiago
Montani, Hugo Santos
author Capriotti, Santiago
author_facet Capriotti, Santiago
Montani, Hugo Santos
author_role author
author2 Montani, Hugo Santos
author2_role author
dc.subject.none.fl_str_mv Integrable Systems
Adler–Kostant–Symes Method
Semidirect Product Lie Algebras
topic Integrable Systems
Adler–Kostant–Symes Method
Semidirect Product Lie Algebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler–Kostant–Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson–Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.
Fil: Capriotti, Santiago. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Montani, Hugo Santos. Universidad Nacional de la Patagonia Austral. Unidad Académica Caleta Olivia. Departamento de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler–Kostant–Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson–Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.
publishDate 2014
dc.date.none.fl_str_mv 2014-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/21691
Capriotti, Santiago; Montani, Hugo Santos; Integrable systems on semidirect product Lie groups; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 47; 206; 5-2014; 1-23
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/21691
identifier_str_mv Capriotti, Santiago; Montani, Hugo Santos; Integrable systems on semidirect product Lie groups; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 47; 206; 5-2014; 1-23
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/47/20/205206/
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/47/20/205206
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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