Wedderburn principal theorem for Jordan superalgebras I

ABSTRACT: We consider finite dimensional Jordan super algebras J over an algebraically closed field of characteristic 0, with solvable radical N such that N 2 = 0 and J/N is a simple Jordan superalgebra of one of the following types: Kac K10, Kaplansky K3, superform or Dt. We prove that an analogue...

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Autores:
Gómez González, Faber Alberto
Tipo de recurso:
Article of investigation
Fecha de publicación:
2018
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/30998
Acceso en línea:
https://hdl.handle.net/10495/30998
Palabra clave:
Jordan superalgebras
Wedderburn Theorem
Decomposition theorem
Semisimple Jordan superalgebras
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/2.5/co/
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oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/30998
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network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv Wedderburn principal theorem for Jordan superalgebras I
title Wedderburn principal theorem for Jordan superalgebras I
spellingShingle Wedderburn principal theorem for Jordan superalgebras I
Jordan superalgebras
Wedderburn Theorem
Decomposition theorem
Semisimple Jordan superalgebras
title_short Wedderburn principal theorem for Jordan superalgebras I
title_full Wedderburn principal theorem for Jordan superalgebras I
title_fullStr Wedderburn principal theorem for Jordan superalgebras I
title_full_unstemmed Wedderburn principal theorem for Jordan superalgebras I
title_sort Wedderburn principal theorem for Jordan superalgebras I
dc.creator.fl_str_mv Gómez González, Faber Alberto
dc.contributor.author.none.fl_str_mv Gómez González, Faber Alberto
dc.subject.proposal.spa.fl_str_mv Jordan superalgebras
Wedderburn Theorem
Decomposition theorem
Semisimple Jordan superalgebras
topic Jordan superalgebras
Wedderburn Theorem
Decomposition theorem
Semisimple Jordan superalgebras
description ABSTRACT: We consider finite dimensional Jordan super algebras J over an algebraically closed field of characteristic 0, with solvable radical N such that N 2 = 0 and J/N is a simple Jordan superalgebra of one of the following types: Kac K10, Kaplansky K3, superform or Dt. We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of N are imposed, where N is considered as a J/N -bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.
publishDate 2018
dc.date.issued.none.fl_str_mv 2018
dc.date.accessioned.none.fl_str_mv 2022-09-30T19:45:55Z
dc.date.available.none.fl_str_mv 2022-09-30T19:45:55Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.type.local.spa.fl_str_mv Artículo de investigación
format http://purl.org/coar/resource_type/c_2df8fbb1
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 0021-8693
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/30998
dc.identifier.doi.none.fl_str_mv 10.1016/j.jalgebra.2018.03.001
dc.identifier.eissn.none.fl_str_mv 1090-266X
identifier_str_mv 0021-8693
10.1016/j.jalgebra.2018.03.001
1090-266X
url https://hdl.handle.net/10495/30998
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournalabbrev.spa.fl_str_mv J. Algebra.
dc.rights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/2.5/co/
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eu_rights_str_mv openAccess
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dc.format.extent.spa.fl_str_mv 32
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Elsevier
dc.publisher.group.spa.fl_str_mv Álgebra U de A
dc.publisher.place.spa.fl_str_mv Nueva York, Estados Unidos
institution Universidad de Antioquia
bitstream.url.fl_str_mv https://bibliotecadigital.udea.edu.co/bitstream/10495/30998/1/Go%cc%81mezF_2018_WedderburnPrincipalTheorem.pdf
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spelling Gómez González, Faber Alberto2022-09-30T19:45:55Z2022-09-30T19:45:55Z20180021-8693https://hdl.handle.net/10495/3099810.1016/j.jalgebra.2018.03.0011090-266XABSTRACT: We consider finite dimensional Jordan super algebras J over an algebraically closed field of characteristic 0, with solvable radical N such that N 2 = 0 and J/N is a simple Jordan superalgebra of one of the following types: Kac K10, Kaplansky K3, superform or Dt. We prove that an analogue of the Wedderburn Principal Theorem (WPT) holds if certain restrictions on the types of irreducible subbimodules of N are imposed, where N is considered as a J/N -bimodule. Using counterexamples, it is shown that the imposed restrictions are essential.COL008689632application/pdfengElsevierÁlgebra U de ANueva York, Estados Unidosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-nd/4.0/Wedderburn principal theorem for Jordan superalgebras IJordan superalgebrasWedderburn TheoremDecomposition theoremSemisimple Jordan superalgebrasJ. Algebra.Journal of Algebra132505ORIGINALGómezF_2018_WedderburnPrincipalTheorem.pdfGómezF_2018_WedderburnPrincipalTheorem.pdfArtículo de investigaciónapplication/pdf574545https://bibliotecadigital.udea.edu.co/bitstream/10495/30998/1/Go%cc%81mezF_2018_WedderburnPrincipalTheorem.pdf110408fb06d9753626ff56730a511165MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8823https://bibliotecadigital.udea.edu.co/bitstream/10495/30998/2/license_rdfb88b088d9957e670ce3b3fbe2eedbc13MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/30998/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/30998oai:bibliotecadigital.udea.edu.co:10495/309982022-09-30 14:45:55.75Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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