Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle

We give a complete description of the anti-involutions of the algebra DN of N X N-matrix differential operators on the circle, preserving the principal ℤ gradation. We obtain, up to conjugation, two families σ±,m with 1≤m≤N, getting two families DN±,m simple Lie subalgebras fixed by -σ±,m. We also g...

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Detalhes bibliográficos
Autores: Boyallian, Carina, Liberati, Jose Ignacio
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2001
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/129961
Acesso em linha:http://hdl.handle.net/11336/129961
Access Level:Acceso aberto
Palavra-chave:Lie algebra
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circleBoyallian, CarinaLiberati, Jose IgnacioLie algebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a complete description of the anti-involutions of the algebra DN of N X N-matrix differential operators on the circle, preserving the principal ℤ gradation. We obtain, up to conjugation, two families σ±,m with 1≤m≤N, getting two families DN±,m simple Lie subalgebras fixed by -σ±,m. We also give a geometric realization of σ±.m, concluding that DN+,m is a subalgebra of DN of type o(m,n) and DN-,m is a subalgebra of DN of type o s p(m,n) (ortho-symplectic). Finally, we study the conformal algebras associated with DN+,m and DN-,m © 2001 American Institute of Physics.Fil: Boyallian, Carina. 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; ArgentinaFil: Liberati, Jose Ignacio. 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; ArgentinaAmerican Institute of Physics2001-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129961Boyallian, Carina; Liberati, Jose Ignacio; Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle; American Institute of Physics; Journal of Mathematical Physics; 42; 8; 8-2001; 3735-37530022-24881089-7658CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.1380252info:eu-repo/semantics/altIdentifier/doi/10.1063/1.1380252info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:20:58Zoai:ri.conicet.gov.ar:11336/129961instacron: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:34982024-05-08 14:20:58.964CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
title Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
spellingShingle Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
Boyallian, Carina
Lie algebra
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
title_full Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
title_fullStr Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
title_full_unstemmed Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
title_sort Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle
dc.creator.none.fl_str_mv Boyallian, Carina
Liberati, Jose Ignacio
author Boyallian, Carina
author_facet Boyallian, Carina
Liberati, Jose Ignacio
author_role author
author2 Liberati, Jose Ignacio
author2_role author
dc.subject.none.fl_str_mv Lie algebra
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Lie algebra
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We give a complete description of the anti-involutions of the algebra DN of N X N-matrix differential operators on the circle, preserving the principal ℤ gradation. We obtain, up to conjugation, two families σ±,m with 1≤m≤N, getting two families DN±,m simple Lie subalgebras fixed by -σ±,m. We also give a geometric realization of σ±.m, concluding that DN+,m is a subalgebra of DN of type o(m,n) and DN-,m is a subalgebra of DN of type o s p(m,n) (ortho-symplectic). Finally, we study the conformal algebras associated with DN+,m and DN-,m © 2001 American Institute of Physics.
publishDate 2001
dc.date.none.fl_str_mv 2001-08
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/11336/129961
Boyallian, Carina; Liberati, Jose Ignacio; Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle; American Institute of Physics; Journal of Mathematical Physics; 42; 8; 8-2001; 3735-3753
0022-2488
1089-7658
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129961
identifier_str_mv Boyallian, Carina; Liberati, Jose Ignacio; Classical Lie subalgebras of the Lie algebra of matrix differential operators on the circle; American Institute of Physics; Journal of Mathematical Physics; 42; 8; 8-2001; 3735-3753
0022-2488
1089-7658
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.1380252
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.1380252
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 American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.811543

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