A note on derivations of lie algebras

M. Shahryari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this note, we will prove that a finite-dimensional Lie algebra L over a field of characteristic zero, admitting an abelian algebra of derivations D≤Der(L), with the property Ln ⊆ ∑d∈D d(L), for some n>1, is necessarily solvable. As a result, we show that if L has a derivation d:L→L such that Ln⊆d(L), for some n>1, then L is solvable.

Original languageEnglish
Pages (from-to)444-446
Number of pages3
JournalBulletin of the Australian Mathematical Society
Volume84
Issue number3
DOIs
Publication statusPublished - Dec 2011
Externally publishedYes

Keywords

  • compact Lie groups
  • derivations
  • Lie algebras
  • solvable Lie algebras

ASJC Scopus subject areas

  • Mathematics(all)

Cite this