Lie 3−algebra and super-affinization of split-octonions

Detalhes bibliográficos
Autor(a) principal: Giardino, Sérgio
Data de Publicação: 2011
Outros Autores: Salazar, Hector Leny Carrion
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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spelling 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:123456789/30849Tk9OLUVYQ0xVU0lWRSBESVNUUklCVVRJT04gTElDRU5TRQoKCkJ5IHNpZ25pbmcgYW5kIGRlbGl2ZXJpbmcgdGhpcyBsaWNlbnNlLCBNci4gKGF1dGhvciBvciBjb3B5cmlnaHQgaG9sZGVyKToKCgphKSBHcmFudHMgdGhlIFVuaXZlcnNpZGFkZSBGZWRlcmFsIFJpbyBHcmFuZGUgZG8gTm9ydGUgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgb2YKcmVwcm9kdWNlLCBjb252ZXJ0IChhcyBkZWZpbmVkIGJlbG93KSwgY29tbXVuaWNhdGUgYW5kIC8gb3IKZGlzdHJpYnV0ZSB0aGUgZGVsaXZlcmVkIGRvY3VtZW50IChpbmNsdWRpbmcgYWJzdHJhY3QgLyBhYnN0cmFjdCkgaW4KZGlnaXRhbCBvciBwcmludGVkIGZvcm1hdCBhbmQgaW4gYW55IG1lZGl1bS4KCmIpIERlY2xhcmVzIHRoYXQgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBpdHMgb3JpZ2luYWwgd29yaywgYW5kIHRoYXQKeW91IGhhdmUgdGhlIHJpZ2h0IHRvIGdyYW50IHRoZSByaWdodHMgY29udGFpbmVkIGluIHRoaXMgbGljZW5zZS4gRGVjbGFyZXMKdGhhdCB0aGUgZGVsaXZlcnkgb2YgdGhlIGRvY3VtZW50IGRvZXMgbm90IGluZnJpbmdlLCBhcyBmYXIgYXMgaXQgaXMKdGhlIHJpZ2h0cyBvZiBhbnkgb3RoZXIgcGVyc29uIG9yIGVudGl0eS4KCmMpIElmIHRoZSBkb2N1bWVudCBkZWxpdmVyZWQgY29udGFpbnMgbWF0ZXJpYWwgd2hpY2ggZG9lcyBub3QKcmlnaHRzLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBvYnRhaW5lZCBhdXRob3JpemF0aW9uIGZyb20gdGhlIGhvbGRlciBvZiB0aGUKY29weXJpZ2h0IHRvIGdyYW50IHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdCB0aGlzIG1hdGVyaWFsIHdob3NlIHJpZ2h0cyBhcmUgb2YKdGhpcmQgcGFydGllcyBpcyBjbGVhcmx5IGlkZW50aWZpZWQgYW5kIHJlY29nbml6ZWQgaW4gdGhlIHRleHQgb3IKY29udGVudCBvZiB0aGUgZG9jdW1lbnQgZGVsaXZlcmVkLgoKSWYgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBiYXNlZCBvbiBmdW5kZWQgb3Igc3VwcG9ydGVkIHdvcmsKYnkgYW5vdGhlciBpbnN0aXR1dGlvbiBvdGhlciB0aGFuIHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBmdWxmaWxsZWQgYW55IG9ibGlnYXRpb25zIHJlcXVpcmVkIGJ5IHRoZSByZXNwZWN0aXZlIGFncmVlbWVudCBvciBhZ3JlZW1lbnQuCgpUaGUgVW5pdmVyc2lkYWRlIEZlZGVyYWwgZG8gUmlvIEdyYW5kZSBkbyBOb3J0ZSB3aWxsIGNsZWFybHkgaWRlbnRpZnkgaXRzIG5hbWUgKHMpIGFzIHRoZSBhdXRob3IgKHMpIG9yIGhvbGRlciAocykgb2YgdGhlIGRvY3VtZW50J3MgcmlnaHRzCmRlbGl2ZXJlZCwgYW5kIHdpbGwgbm90IG1ha2UgYW55IGNoYW5nZXMsIG90aGVyIHRoYW4gdGhvc2UgcGVybWl0dGVkIGJ5CnRoaXMgbGljZW5zZQo=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
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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
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