Gradings induced by nilpotent elements

The authors express their sincere thanks to the anonymous expert referee for the careful reading of the manuscript and his/her competent and insightful comments and suggestions.

Detalhes bibliográficos
Autores: García, Esther, Gómez Lozano, Miguel, Muñoz Alcázar, Rubén, Vera de Salas, Guillermo
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/24475
Acesso em linha:https://hdl.handle.net/10115/24475
Access Level:acceso abierto
Palavra-chave:von Neumann regular
Nilpotent element
Grading
sl2-triple
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oai_identifier_str oai:burjcdigital.urjc.es:10115/24475
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repository_id_str
spelling Gradings induced by nilpotent elementsGarcía, EstherGómez Lozano, MiguelMuñoz Alcázar, RubénVera de Salas, Guillermovon Neumann regularNilpotent elementGradingsl2-tripleThe authors express their sincere thanks to the anonymous expert referee for the careful reading of the manuscript and his/her competent and insightful comments and suggestions.An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars Φ gives rise to a complete system of orthogonal idempotents that induces a finite Z-grading on R; we also show that such element gives rise to an sl2-triple in R with semisimple adjoint map adh, and that the grading of R with respect to the complete system of orthogonal idempotents is a refinement of the Φgrading induced by the eigenspaces of adh. These results can be adapted to nilpotent elements a with all their powers von Neumann regular, in which case the element a can be completed to an sl2-triple and a is homogeneous of degree 2 both in the Z-grading of R and in the Φ-grading given by the eigenspaces of adh.Elsevier202320232022info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/24475reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/244752026-06-24T12:48:17Z
dc.title.none.fl_str_mv Gradings induced by nilpotent elements
title Gradings induced by nilpotent elements
spellingShingle Gradings induced by nilpotent elements
García, Esther
von Neumann regular
Nilpotent element
Grading
sl2-triple
title_short Gradings induced by nilpotent elements
title_full Gradings induced by nilpotent elements
title_fullStr Gradings induced by nilpotent elements
title_full_unstemmed Gradings induced by nilpotent elements
title_sort Gradings induced by nilpotent elements
dc.creator.none.fl_str_mv García, Esther
Gómez Lozano, Miguel
Muñoz Alcázar, Rubén
Vera de Salas, Guillermo
author García, Esther
author_facet García, Esther
Gómez Lozano, Miguel
Muñoz Alcázar, Rubén
Vera de Salas, Guillermo
author_role author
author2 Gómez Lozano, Miguel
Muñoz Alcázar, Rubén
Vera de Salas, Guillermo
author2_role author
author
author
dc.subject.none.fl_str_mv von Neumann regular
Nilpotent element
Grading
sl2-triple
topic von Neumann regular
Nilpotent element
Grading
sl2-triple
description The authors express their sincere thanks to the anonymous expert referee for the careful reading of the manuscript and his/her competent and insightful comments and suggestions.
publishDate 2022
dc.date.none.fl_str_mv 2022
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/24475
url https://hdl.handle.net/10115/24475
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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