A note on derivations of lie algebras

M. Shahryari

doi:10.1017/S0004972711002516

A note on derivations of lie algebras

M. Shahryari^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	444-446
Number of pages	3
Journal	Bulletin of the Australian Mathematical Society
Volume	84
Issue number	3
DOIs	https://doi.org/10.1017/S0004972711002516
Publication status	Published - Dec 2011
Externally published	Yes

Keywords

Lie algebras
compact Lie groups
derivations
solvable Lie algebras

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S0004972711002516

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AB - 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.

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KW - compact Lie groups

KW - derivations

KW - solvable Lie algebras

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A note on derivations of lie algebras

Abstract

Keywords

ASJC Scopus subject areas

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