Lie 3−algebra and super-affinization of split-octonions
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30849 |
Resumo: | The purpose of this study is to extend the concept of a generalized Lie 3− algebra, known to the divisional algebra of the octonions O, to split-octonions SO, which is non-divisional. This is achieved through the unification of the product of both of the algebras in a single operation. Accordingly, a notational device is introduced to unify the product of both algebras. We verify that SO is a Malcev algebra and we recalculate known relations for the structure constants in terms of the introduced structure tensor. Finally we construct the manifestly super-symmetric N = 1 SO affine super-algebra. An application of the split Lie 3−algebra for a Bagger and Lambert gauge theory is also discussed |
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Giardino, SérgioSalazar, Hector Leny Carrion2020-12-07T12:57:04Z2020-12-07T12:57:04Z2011-05-18CARRIÓN, Hector L.; GIARDINO, Sergio. Lie 3−algebra and super-affinization of split-octonions. Modern Physics Letters A, [S.L.], v. 26, n. 35, p. 2663-2675, 20 nov. 2011. Disponível em: http://old.inspirehep.net/record/853065?ln=pt. Acesso em: 20 nov. 2020. http://dx.doi.org/10.1142/s0217732311037005.0217-73231793-6632https://repositorio.ufrn.br/handle/123456789/3084910.1142/s0217732311037005World Scientific PublishingAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessLie algebraGauge field theoryOctonionLie 3−algebra and super-affinization of split-octonionsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleThe purpose of this study is to extend the concept of a generalized Lie 3− algebra, known to the divisional algebra of the octonions O, to split-octonions SO, which is non-divisional. This is achieved through the unification of the product of both of the algebras in a single operation. Accordingly, a notational device is introduced to unify the product of both algebras. We verify that SO is a Malcev algebra and we recalculate known relations for the structure constants in terms of the introduced structure tensor. Finally we construct the manifestly super-symmetric N = 1 SO affine super-algebra. An application of the split Lie 3−algebra for a Bagger and Lambert gauge theory is also discussedengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALLie 3−algebra_SALAZAR_2010.pdfLie 3−algebra_SALAZAR_2010.pdfArtigoapplication/pdf188078https://repositorio.ufrn.br/bitstream/123456789/30849/1/Lie%203%e2%88%92algebra_SALAZAR_2010.pdf3e03bb7b9dd89aa7035cc8f5f0b27d7cMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufrn.br/bitstream/123456789/30849/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30849/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTLie 3−algebra_SALAZAR_2010.pdf.txtLie 3−algebra_SALAZAR_2010.pdf.txtExtracted texttext/plain30006https://repositorio.ufrn.br/bitstream/123456789/30849/4/Lie%203%e2%88%92algebra_SALAZAR_2010.pdf.txtebc9f87c69ed818e85735a409e75d396MD54THUMBNAILLie 3−algebra_SALAZAR_2010.pdf.jpgLie 3−algebra_SALAZAR_2010.pdf.jpgGenerated Thumbnailimage/jpeg1554https://repositorio.ufrn.br/bitstream/123456789/30849/5/Lie%203%e2%88%92algebra_SALAZAR_2010.pdf.jpg7c0ba073d987d3c69f427f3316b55c70MD55123456789/308492020-12-13 05:01:37.349oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-12-13T08:01:37Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Lie 3−algebra and super-affinization of split-octonions |
title |
Lie 3−algebra and super-affinization of split-octonions |
spellingShingle |
Lie 3−algebra and super-affinization of split-octonions Giardino, Sérgio Lie algebra Gauge field theory Octonion |
title_short |
Lie 3−algebra and super-affinization of split-octonions |
title_full |
Lie 3−algebra and super-affinization of split-octonions |
title_fullStr |
Lie 3−algebra and super-affinization of split-octonions |
title_full_unstemmed |
Lie 3−algebra and super-affinization of split-octonions |
title_sort |
Lie 3−algebra and super-affinization of split-octonions |
author |
Giardino, Sérgio |
author_facet |
Giardino, Sérgio Salazar, Hector Leny Carrion |
author_role |
author |
author2 |
Salazar, Hector Leny Carrion |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Giardino, Sérgio Salazar, Hector Leny Carrion |
dc.subject.por.fl_str_mv |
Lie algebra Gauge field theory Octonion |
topic |
Lie algebra Gauge field theory Octonion |
description |
The purpose of this study is to extend the concept of a generalized Lie 3− algebra, known to the divisional algebra of the octonions O, to split-octonions SO, which is non-divisional. This is achieved through the unification of the product of both of the algebras in a single operation. Accordingly, a notational device is introduced to unify the product of both algebras. We verify that SO is a Malcev algebra and we recalculate known relations for the structure constants in terms of the introduced structure tensor. Finally we construct the manifestly super-symmetric N = 1 SO affine super-algebra. An application of the split Lie 3−algebra for a Bagger and Lambert gauge theory is also discussed |
publishDate |
2011 |
dc.date.issued.fl_str_mv |
2011-05-18 |
dc.date.accessioned.fl_str_mv |
2020-12-07T12:57:04Z |
dc.date.available.fl_str_mv |
2020-12-07T12:57:04Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CARRIÓN, Hector L.; GIARDINO, Sergio. Lie 3−algebra and super-affinization of split-octonions. Modern Physics Letters A, [S.L.], v. 26, n. 35, p. 2663-2675, 20 nov. 2011. Disponível em: http://old.inspirehep.net/record/853065?ln=pt. Acesso em: 20 nov. 2020. http://dx.doi.org/10.1142/s0217732311037005. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30849 |
dc.identifier.issn.none.fl_str_mv |
0217-7323 1793-6632 |
dc.identifier.doi.none.fl_str_mv |
10.1142/s0217732311037005 |
identifier_str_mv |
CARRIÓN, Hector L.; GIARDINO, Sergio. Lie 3−algebra and super-affinization of split-octonions. Modern Physics Letters A, [S.L.], v. 26, n. 35, p. 2663-2675, 20 nov. 2011. Disponível em: http://old.inspirehep.net/record/853065?ln=pt. Acesso em: 20 nov. 2020. http://dx.doi.org/10.1142/s0217732311037005. 0217-7323 1793-6632 10.1142/s0217732311037005 |
url |
https://repositorio.ufrn.br/handle/123456789/30849 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
World Scientific Publishing |
publisher.none.fl_str_mv |
World Scientific Publishing |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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UFRN |
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