Lie algebras with complemented ideals. (Ukrainian. English summary) Zbl 1101.17004
Summary: We investigate finite dimensional Lie algebras \(L\) over an algebraically closed field of characteristic 0 which split over their arbitrary ideals (i.e. in which for every ideal \(I\) there exists a subalgebra \(A\) such that \(L = I + A, I\cap A = 0\)). It turns out in particular that in the solvable case all subalgebras of such algebras are complemented and non-solvable Lie algebras of such type contain an Abelian ideal which is complemented by a reductive subalgebra.
MSC:
17B05 | Structure theory for Lie algebras and superalgebras |
17B30 | Solvable, nilpotent (super)algebras |