Ideals and primitive elements of some relatively free Lie algebras

Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] th...

Descripción completa

Detalles Bibliográficos
Autores principales: Ekici, Naime, Esmerligil, Zerrin, Ersalan, Dilek
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4917519/
https://www.ncbi.nlm.nih.gov/pubmed/27386282
http://dx.doi.org/10.1186/s40064-016-2545-2
_version_ 1782438949423153152
author Ekici, Naime
Esmerligil, Zerrin
Ersalan, Dilek
author_facet Ekici, Naime
Esmerligil, Zerrin
Ersalan, Dilek
author_sort Ekici, Naime
collection PubMed
description Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism.
format Online
Article
Text
id pubmed-4917519
institution National Center for Biotechnology Information
language English
publishDate 2016
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-49175192016-07-06 Ideals and primitive elements of some relatively free Lie algebras Ekici, Naime Esmerligil, Zerrin Ersalan, Dilek Springerplus Research Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism. Springer International Publishing 2016-06-22 /pmc/articles/PMC4917519/ /pubmed/27386282 http://dx.doi.org/10.1186/s40064-016-2545-2 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Ekici, Naime
Esmerligil, Zerrin
Ersalan, Dilek
Ideals and primitive elements of some relatively free Lie algebras
title Ideals and primitive elements of some relatively free Lie algebras
title_full Ideals and primitive elements of some relatively free Lie algebras
title_fullStr Ideals and primitive elements of some relatively free Lie algebras
title_full_unstemmed Ideals and primitive elements of some relatively free Lie algebras
title_short Ideals and primitive elements of some relatively free Lie algebras
title_sort ideals and primitive elements of some relatively free lie algebras
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4917519/
https://www.ncbi.nlm.nih.gov/pubmed/27386282
http://dx.doi.org/10.1186/s40064-016-2545-2
work_keys_str_mv AT ekicinaime idealsandprimitiveelementsofsomerelativelyfreeliealgebras
AT esmerligilzerrin idealsandprimitiveelementsofsomerelativelyfreeliealgebras
AT ersalandilek idealsandprimitiveelementsofsomerelativelyfreeliealgebras

Ejemplares similares