Ideals and primitive elements of some relatively free Lie algebras

Ekici N., Esmerligil Z., Ersalan D.

SPRINGERPLUS, vol.5, 2016 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 5
  • Publication Date: 2016
  • Doi Number: 10.1186/s40064-016-2545-2
  • Journal Name: SPRINGERPLUS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Çukurova University Affiliated: Yes

Abstract

Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal <(v) over tilde > of the algebra F/gamma(m+1) (F') contains a primitive element (u) over tilde then the element (v) over tilde is primitive. We also show that, in the Lie algebra F/gamma(3)(F)' there exists an element (v) over bar such that the ideal <(v) over bar > contains a primitive element (u) over bar but, (u) over bar and (v) over bar are not conjugate by means of an inner automorphism.