Composition algebras and the two faces of G2

We consider composition and division algebras over the real numbers: We note two roles for the group G2: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams th...

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Detalles Bibliográficos
Autores: Boya, Luis J., Campoamor Stursberg, Otto-Rudwig
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/43761
Acceso en línea:https://hdl.handle.net/20.500.14352/43761
Access Level:acceso abierto
Palabra clave:512
First exceptional Lie group G2
Composition algebra
Division algebra
Octonions
Automorphism group of octonions
Isotropy group
Quaternions
Split octonions
Tensors
Spin groups
F4
Álgebra
1201 Álgebra
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spelling Composition algebras and the two faces of G2Boya, Luis J.Campoamor Stursberg, Otto-Rudwig512First exceptional Lie group G2Composition algebraDivision algebraOctonionsAutomorphism group of octonionsIsotropy groupQuaternionsSplit octonionsTensorsSpin groupsF4Álgebra1201 ÁlgebraWe consider composition and division algebras over the real numbers: We note two roles for the group G2: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.World ScientificUniversidad Complutense de Madrid20102010-01-0120102010-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/43761reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/437612026-06-02T12:44:21Z
dc.title.none.fl_str_mv Composition algebras and the two faces of G2
title Composition algebras and the two faces of G2
spellingShingle Composition algebras and the two faces of G2
Boya, Luis J.
512
First exceptional Lie group G2
Composition algebra
Division algebra
Octonions
Automorphism group of octonions
Isotropy group
Quaternions
Split octonions
Tensors
Spin groups
F4
Álgebra
1201 Álgebra
title_short Composition algebras and the two faces of G2
title_full Composition algebras and the two faces of G2
title_fullStr Composition algebras and the two faces of G2
title_full_unstemmed Composition algebras and the two faces of G2
title_sort Composition algebras and the two faces of G2
dc.creator.none.fl_str_mv Boya, Luis J.
Campoamor Stursberg, Otto-Rudwig
author Boya, Luis J.
author_facet Boya, Luis J.
Campoamor Stursberg, Otto-Rudwig
author_role author
author2 Campoamor Stursberg, Otto-Rudwig
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512
First exceptional Lie group G2
Composition algebra
Division algebra
Octonions
Automorphism group of octonions
Isotropy group
Quaternions
Split octonions
Tensors
Spin groups
F4
Álgebra
1201 Álgebra
topic 512
First exceptional Lie group G2
Composition algebra
Division algebra
Octonions
Automorphism group of octonions
Isotropy group
Quaternions
Split octonions
Tensors
Spin groups
F4
Álgebra
1201 Álgebra
description We consider composition and division algebras over the real numbers: We note two roles for the group G2: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01
2010
2010-01-01
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/20.500.14352/43761
url https://hdl.handle.net/20.500.14352/43761
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 World Scientific
publisher.none.fl_str_mv World Scientific
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
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score 15,300719

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