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...

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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
Descripción
Sumario: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.

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