Characterization of 9-dimensional Anosov Lie Algebras

Autores
Mainkar, Meera; Will, Cynthia Eugenia
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. In this paper we study 9 -dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3 -step Anosov Lie algebra of dimension 9. In the 2 -step case, we prove that a 2 -step 9 -dimensional Anosov Lie algebra with no abelian factor must have a 3 -dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.
Fil: Mainkar, Meera. Michigan State University; Estados Unidos
Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Anosov
Diffeomorphism
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:11336/51753
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Characterization of 9-dimensional Anosov Lie AlgebrasMainkar, MeeraWill, Cynthia EugeniaAnosovDiffeomorphismhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. In this paper we study 9 -dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3 -step Anosov Lie algebra of dimension 9. In the 2 -step case, we prove that a 2 -step 9 -dimensional Anosov Lie algebra with no abelian factor must have a 3 -dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.Fil: Mainkar, Meera. Michigan State University; Estados UnidosFil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaHeldermann Verlag2015-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/51753Mainkar, Meera; Will, Cynthia Eugenia; Characterization of 9-dimensional Anosov Lie Algebras; Heldermann Verlag; Journal Of Lie Theory; 25; 3; 9-2015; 857-8730949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT25/JLT253/jlt25040.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T15:52:47Zoai:ri.conicet.gov.ar:11336/51753instacron: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:34982026-08-25 15:52:48.586CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Characterization of 9-dimensional Anosov Lie Algebras
title Characterization of 9-dimensional Anosov Lie Algebras
spellingShingle Characterization of 9-dimensional Anosov Lie Algebras
Mainkar, Meera
Anosov
Diffeomorphism
title_short Characterization of 9-dimensional Anosov Lie Algebras
title_full Characterization of 9-dimensional Anosov Lie Algebras
title_fullStr Characterization of 9-dimensional Anosov Lie Algebras
title_full_unstemmed Characterization of 9-dimensional Anosov Lie Algebras
title_sort Characterization of 9-dimensional Anosov Lie Algebras
dc.creator.none.fl_str_mv Mainkar, Meera
Will, Cynthia Eugenia
author Mainkar, Meera
author_facet Mainkar, Meera
Will, Cynthia Eugenia
author_role author
author2 Will, Cynthia Eugenia
author2_role author
dc.subject.none.fl_str_mv Anosov
Diffeomorphism
topic Anosov
Diffeomorphism
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. In this paper we study 9 -dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3 -step Anosov Lie algebra of dimension 9. In the 2 -step case, we prove that a 2 -step 9 -dimensional Anosov Lie algebra with no abelian factor must have a 3 -dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.
Fil: Mainkar, Meera. Michigan State University; Estados Unidos
Fil: Will, Cynthia Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description The classification of all real and rational Anosov Lie algebras up to dimension 8 is given by Lauret and Will. In this paper we study 9 -dimensional Anosov Lie algebras by using the properties of very special algebraic numbers and Lie algebra classification tools. We prove that there exists a unique, up to isomorphism, complex 3 -step Anosov Lie algebra of dimension 9. In the 2 -step case, we prove that a 2 -step 9 -dimensional Anosov Lie algebra with no abelian factor must have a 3 -dimensional derived algebra and we characterize these Lie algebras in terms of their Pfaffian forms. Among these Lie algebras, we exhibit a family of infinitely many complex non-isomorphic Anosov Lie algebras.
publishDate 2015
dc.date.none.fl_str_mv 2015-09
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/11336/51753
Mainkar, Meera; Will, Cynthia Eugenia; Characterization of 9-dimensional Anosov Lie Algebras; Heldermann Verlag; Journal Of Lie Theory; 25; 3; 9-2015; 857-873
0949-5932
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51753
identifier_str_mv Mainkar, Meera; Will, Cynthia Eugenia; Characterization of 9-dimensional Anosov Lie Algebras; Heldermann Verlag; Journal Of Lie Theory; 25; 3; 9-2015; 857-873
0949-5932
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://www.heldermann.de/JLT/JLT25/JLT253/jlt25040.htm
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 Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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 13.334379

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