TY - JOUR
T1 - A note on derivations of lie algebras
AU - Shahryari, M.
PY - 2011/12
Y1 - 2011/12
N2 - 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.
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.
KW - Lie algebras
KW - compact Lie groups
KW - derivations
KW - solvable Lie algebras
UR - http://www.scopus.com/inward/record.url?scp=80455150438&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80455150438&partnerID=8YFLogxK
U2 - 10.1017/S0004972711002516
DO - 10.1017/S0004972711002516
M3 - Article
AN - SCOPUS:80455150438
SN - 0004-9727
VL - 84
SP - 444
EP - 446
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -